Plz help me ASAP it’s important

Answer:

a) H0:μ=55,000 H1:μ>55,000

b) Yes, since we can can reject the null hypothesis

Step-by-step explanation:

a) The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

For this case;

Null hypothesis is that the starting salary will be equal to $55,000/year.

H0:μ=55,000

Alternative hypothesis is that the starting salary will be greater than $55,000/year.

H1:μ>55,000

b) Decision Rule;

P-value > significance level --- accept Null hypothesis

P-value < significance level --- reject Null hypothesis

For this case;

P-value = 0.0392

α = 0.05

Since P-value < 0.05, we can reject null hypothesis.

Therefore, we can accept alternative hypothesis which is the starting salary will be greater than $55,000/year, so the student should pursue an actuary career because the starting salary will be greater than $55,000/year.

- Yes, since we can can reject the null hypothesis

Answer:

Step-by-step explanation:

Hello!

The variable is

X: average mass of a sample of rocks collected in the waters of a region. (measured in grams)

Variables can be:

Quantitative: they represent number, any characteristic that can be "counted" is a quantitative variable, the most common examples are weight, volume, temperature, height, etc...

There are two types of quantitative variables:

⇒ Discrete variables: The only take certain values within the interval of definition of the variable, for example "number of sales" or "money in a wallet"

⇒ Continuous variables: They can take any value within an interval, in this example that you are working with mass, depending on the precision of the scale the mass can have infinite decimal values.

Qualitative: they represent characteristics that cannot be counted, meaning, they are not represented by numbers. There are many attributes that are qualitative variables, for example: colors, race of an animal, phenotypes, types of business, etc...

1)

The variable in this example is Quantitative, it takes numerical values, and the correct option is:

D. Quantitative, because numerical values, found by either measuring or counting, are used to describe the data.

2)

The values of mass of the rocks can take any value within the range of definition of the variable, they only depend on the precision of the scale used to weight the rocks.

B. Interval, because the differences in the data can be meaningfully measured, but the data do not have a true zero point.

3)

A standard 52-card deck contains 13 cards for each suit (clubs, diamonds, hearts and spades)

To calculate the probability of choosing a card at random and it being a Diamond, supposing that all cards are equally probable, you have to divide the total number of diamonds by the total number of cards in the deck:

P(diamond)= 13/52= 0.25

For items 4) and 5) the contingency tables are attached.

4)

a. and b. are conditional probabilities, to calculate them you have to apply the following formula: [tex]P(A|B)= \frac{P(AnB)}{P(B)}[/tex]

This means that the probability of the event "A" given that event "B" has occurred is equal to the probability of the intersection between events "A" and "B" divided by the probability of event "B"

a. P(A|C)= [tex]\frac{P(AnC)}{P(C)}[/tex]

To calculate the probability of the intersection P(A∩C) you have to divide the observations where both events cross by the total of observations on the table:

P(A∩C)= 10/50= 0.20

The probability of C is found in the margins of the table, in this case you have to divide the total of observations for event C by the total of observations of the table:

P(C)= 21/50= 0.42

Now you can calculate the asked probability:

[tex]P(A|C)= \frac{0.2}{0.42}= 0.48[/tex]

b. P(C|A)= [tex]\frac{P(AnC)}{P(A)}[/tex]

From item a. we already know that P(A∩C)= 10/50= 0.20

The probability of event A is  in the margin of the table and you calculate it as:

P(A)= 27/50= 0.54

Then:

[tex]P(C|A)= \frac{0.20}{0.54} = 0.37[/tex]

c. P(BE)

This symbolized the probability of the events "B" and "E" occurring at the same time, you can also symbolize it as P(B∩E)

To calculate the probability of B and E happening you have to do as follows:

P(B∩E)= 8/50= 0.16

5)

a. P(C|A)= 0.37 (As calculated in 4b.)

b. P(BE) and c. P(EB) ⇒ Both expressions symbolize the intersection between events "B" and "E", P(B∩E)= P(E∩B)= 0.16 (As calculated in 4c.)

I hope this helps!

Answer:

Distance from the base of the cliff to the point on the ground = 7608 feet

Step-by-step explanation:

Given: Height of the cliff is 532 feet, angle of depression from the top of the cliff to a point on the ground is equal to 4 degrees.

To find: distance from the base of the cliff to the point on the ground

Solution:

In ΔABC,

[tex]\angle ACB=4^{\circ}[/tex]  (Alternate interior angles)

For any angle [tex]\theta[/tex], [tex]\tan \theta =[/tex] side opposite to angle/side adjacent to angle

[tex]\tan C=\frac{AB}{BC}[/tex]

Put [tex]AB=532\,,\,\angle C=4^{\circ}[/tex]

[tex]\tan 4^{\circ}=\frac{532}{BC}\\\\BC=\frac{532}{\tan 4^{\circ}}\\\\=7607.95\\\\\approx 7608\,\,feet[/tex]

Distance from the base of the cliff to the point on the ground = 7608 feet

Answer:

a rigt angle is a total of 90 degrees so subtratct 51 from 90 and you get 39 degrees.

Answer:

The inter-decile range of IQ is 40.96.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 100, \sigma = 16[/tex]

First decile:

100/10 = 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.28 = \frac{X - 100}{16}[/tex]

[tex]X - 100 = -1.28*16[/tex]

[tex]X = 79.52[/tex]

Ninth decile:

9*(100/10) = 90th percentile, which is X when Z has a pvalue of 0.9. So it is X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 100}{16}[/tex]

[tex]X - 100 = 1.28*16[/tex]

[tex]X = 120.48[/tex]

Interdecile range:

120.48 - 79.52 = 40.96

The inter-decile range of IQ is 40.96.

Answer:

(a) 5* 10¹⁰ (b) 5* 10⁴ particles / m²

Step-by-step explanation:

Solution

(a) We find the number of particles that is created

Now,

The energy will change into particles of masses that is averaging  200 MeV/c²

The number of particles that were created is stated as follows:

n = Ec/Er

Ec =This is the cosmic energy

Er =The rest mass energy

Thus, we  replace 10¹⁰ with Ec and (0.200 GeV/c²)c² for Er

This gives us the following:

n = 10¹⁰ GeV/ (0.200 GeV/c²)c²

= 5* 10¹⁰

Hence the number of particle created is 5* 10¹⁰

(b) We now find how many particles are there per square meter

Thus,

n/m² = 5* 10¹⁰ particles/(1000 m)²

= 5* 10⁴ particles / m²

Hence, the particles that are there per square meter is 5* 10⁴ particles / m²

Note: Kindly find an attached copy of the complete question to this solution below.

Answer:

The slope of AB is

different than the

slope of BC.

Step-by-step explanation:

Answer:

Probability that one of the giftcards will go to a student athlete and one will go to a freshman = 26.4%

Step-by-step explanation:

At Central High School, 55% of students play a school sport. Also, 24% of the student population is in ninth grade. No ninth graders are allowed to play school sports. If two students are selected at random to receive a gift card, what is the probability that one will go to a student athlete and one will go to a freshman? Write the answer as a percent rounded to the nearest tenth of a percent.

Solution

Probability that a student plays a school sport, that is, probability that a student is a student athlete = P(S) = 55% = 0.55

Probability that a student is in the ninth grade, that is, probability that a student is a freshman = P(F) = 24% = 0.24

It was given that no freshman is allowed to play sports, hence, it translates that the event that a student is a student athlete and the event that a student is a freshman are mutually exclusive.

P(S n F) = 0

If two students are then picked at random to receive a gift card, we require the probability that one will go to a student athlete and one will go to a freshman.

Probability that the first one goes to a student athlete = P(S) = 0.55

Probability that the second one goes to a freshman ≈ 0.24

Probability that the first one goes to a freshman = P(F) = 0.24

Probability that the second one goes to a student athlete ≈ 0.55

Probability that one will go to a student athlete and one will go to a freshman

= (0.55 × 24) + (0.24 × 0.55)

= 0.132 + 0.132

= 0.264

= 26.4% in percent to the nearest tenth.

Hope this Helps!!

Answer:

n = -1

Step-by-step explanation:

So first subtract 9 to both sides

8n = -n - 9

Now you want the n on one side and the constant on the other

so add the single n to the n side

9n = -9

Divide 9 to both sides to solve for n

n = -1

Answer:

Step-by-step explanation:

What function ?

Answer:

Find the sales (in units) needed to earn a profit of $262,500

Step-by-step explanation:

hope this is helpful to you bro

Answer:

[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]  

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55.

Step-by-step explanation:

Information given

We have the following data: 54 55 58 59 59 60 61 61 62 65

The sample mean and deviation can be calculated with the following formulas:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X-i -\bar x)^2}{n-1}}[/tex]

[tex]\bar X=59.4[/tex] represent the sample mean

[tex]s=3.239[/tex] represent the sample standard deviation

[tex]n=10[/tex] sample size  

[tex]\alpha=0.05[/tex] represent the significance level

t would represent the statistic  

[tex]p_v[/tex] represent the p value

System of hypothesis

We want to test if the true mean is higher than 55, the system of hypothesis would be:  

Null hypothesis:[tex]\mu \leq 55[/tex]  

Alternative hypothesis:[tex]\mu > 55[/tex]  

Replacing the info given we got:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

And replacing the info given we got:

[tex]t=\frac{59.4-55}{\frac{3.239}{\sqrt{10}}}=4.296[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=10-1=9[/tex]  

The p value for this case is given by:

[tex]p_v =P(t_{(9)}>4.296)=0.001[/tex]  

And for this case the p value is lower than the significance level so we have enough evidence to reject the null hypothesis and then we can conclude that true mean is higher than 55

Answer:

step 3 is wrong

Step-by-step explanation:

i know it because i did the unit test review

Answer:

D

ヾ(•ω•`)o

Step-by-step explanation:

Answer:

the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

Step-by-step explanation:

Let assume that n should represent the number of the students

SO, [tex]\bar x[/tex] can now be the sample mean of number of students  in GPA's

To obtain n such that [tex]P( \bar x \leq 2.3 ) \leq .04[/tex]

⇒ [tex]P( \bar x \geq 2.3 ) \geq .96[/tex]

However ;

[tex]E(x) = \int\limits^4_2 Dx (2+e^{-x} ) 4x = D \\ \\ = D(e^{-x} (e^xx^2 - x-1 ) ) ^D_2 = 12.314 D[/tex]

[tex]E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D[/tex]

Similarly;

[tex]D\int\limits^4_2(2+ e^{-x}) dx = 1[/tex]

⇒ [tex]D*(2x-e^{-x} ) |^4_2 = 1[/tex]

⇒ [tex]D*4.117 = 1[/tex]

⇒ [tex]D= \dfrac{1}{4.117}[/tex]

[tex]\mu = E(x) = 2.991013 ; \\ \\ E(x^2) = 9.28103[/tex]

∴  [tex]Var (x) = E(x^2) - E^2(x) \\ \\ = .3348711[/tex]

Now; [tex]P(\bar \geq 2.3) = P( \bar x - 2.991013 \geq 2.3 - 2.991013) \\ \\ = P( \omega \geq .691013) \ \ \ \ \ \ \ \ \ \ (x = E(\bar x ) - \mu)[/tex]

Using Chebysher one sided inequality ; we have:

[tex]P(\omega \geq -.691013) \geq \dfrac{(.691013)^2}{Var ( \omega) +(.691013)^2}[/tex]

So; [tex](\omega = \bar x - \mu)[/tex]

⇒ [tex]E(\omega ) = 0 \\ \\ Var (\omega ) = \dfrac{Var (x_i)}{n}[/tex]

∴ [tex]P(\omega \geq .691013) \geq \dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2}[/tex]

To determine n; such that ;

[tex]\dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2} \geq 0.96 \\ \\ \\ (.691013)^2(1-.96) \geq \dfrac{-3348711*.96}{n}[/tex]

⇒ [tex]n \geq \dfrac{.3348711*.96}{.04*(.691013)^2}[/tex]

[tex]n \geq 16.83125[/tex]

Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

Answer:

Height of the Dom is 112.18 m.

Step-by-step explanation:

The tallest church tower in the Netherlands is the Dom Tower in Utrecht. The angle of elevation to the top of the tower is 77° when 25.9 m from the base. It is required to find the height of the Dom Tower. Let its height is h. So, using trigonometric formula to find it as :

[tex]\tan\theta=\dfrac{h}{b}\\\\\tan(77)=\dfrac{h}{25.9}\\\\h=\tan(77)\times 25.9\\\\h=112.18\ m[/tex]

So, the height of the Dom is 112.18 m.

Answer:it is b

Step-by-step explanation:

Answer:

a) x = 30°

b) mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

Question:

The complete question as found on Chegg website:

In the diagram below, secants PT and PU have been drawn from exterior point P such that the four arcs

intercepted have the following ratio of measurements:

mRS : mST :MTU : mUR=1:4:4:3

(a) If mRS = x, then write an equation that could be used to solve for x

and find the value of x.

(b) State the measure of each of the four arcs.

mRS =

mST =

MTU

MUR =

Step-by-step explanation:

Find attached the diagram related to the question

mRS : mST : mTU : mUR = 1:4:4:3

Since mRS = x

Writing the ratios of the measure of angle in terms of mRS:

mST = 4× mRS = 4×x = 4x

mTU = 4× mRS = 4×x = 4x

mUR= 3× mRS = 3×x = 3x

The sum of measure the 4 measures of arc = 360° (sum of angle in a circle)

mRS + mST + mTU + mUR = 360°

x + 4x + 4x + 3x = 360

12x = 360

x = 360/12

x = 30°

b) The measure of angle

mRS = x = 30°

mST = 4x = 4(30°) = 120°

mTU = 4x = 4(30°) = 120°

mUR = 3x = 3(30°) = 90°

Answer:

[tex]\sqrt{-6} \sqrt{-384}=\sqrt{(-6)(-384)}=\sqrt{2304}=48\\ a=48\\b=0[/tex]

or

[tex]a=-48\\b=0[/tex]

both solutions are correct because root square has two solutions, one positive and one negative.

Answer:

a= -48

b=0

Step-by-step explanation:

[tex]\sqrt[]{-6} = i\sqrt{6}[/tex]

[tex]\sqrt{-384} =i\sqrt{384}[/tex]

[tex](i\sqrt{6} )(i\sqrt{384} )[/tex]

[tex]i^{2} \sqrt{2304}[/tex]

(-1)(48) = -48

a + bi

a= -48

b= 0

Answer:

a) N(2617, 586)

b) 0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c) 0.4013 = 40.13% of the customers consume over 2764 calories

d) 3981 calories.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 2617, \sigma = 586[/tex]

a. What is the distribution of X?

Here we first place the mean, then the standard deviation.

N(2617, 586)

b. Find the probability that the customer consumes less than 2409 calories.

This is the pvalue of Z when X = 2409. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2409 - 2617}{586}[/tex]

[tex]Z = -0.355[/tex]

[tex]Z = -0.355[/tex] has a pvalue of 0.3613

0.3613 = 36.13% probability that the customer consumes less than 2409 calories.

c. What proportion of the customers consume over 2764 calories?

This is 1 subtracted by the pvalue of Z when X = 2764. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{2764 - 2617}{586}[/tex]

[tex]Z = 0.25[/tex]

[tex]Z = 0.25[/tex] has a pvalue of 0.5987

1 - 0.5987 = 0.4013

0.4013 = 40.13% of the customers consume over 2764 calories

d. The Piggy award will given out to the 1% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?

Top 1%, so the 100-1 = 99th percentile.

The 99th percentile is the value of X when Z has a pvalue of 0.99. So it is X when Z = 2.327. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]2.327 = \frac{X - 2617}{586}[/tex]

[tex]X - 2617 = 2.327*586[/tex]

[tex]X = 3980.6[/tex]

Rounding to the nearest calorie, 3981 calories.

Answer:

49

Step-by-step explanation:

Positive 49 not -49

Answer:

You can do this two ways

1. Divide 170 into 4 parts and multiply by 3.

170/4=42.5

42.5 x 3 = 127.5 so 127.5 is the answer

2. 3/4=0.75

170 x 0.75 = 127.5

or 170/1 x 3/4 = 510/4 = 127 1/2

127 1/2 = 127.5 because 1 divided by 2 is 0.5__127 + 0.5 = 127.5

Hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question is incomplete. The missing data is:

30, 155, 205, 235, 180, 235, 70, 250, 135, 145, 225, 230, 30

Solution:

Mean = (30 + 155 + 205 + 235 + 180 + 235 + 70 + 250 + 135 + 145 + 225 + 230 + 30)/13 = 163.5

Standard deviation = √(summation(x - mean)²/n

n = 13

Summation(x - mean)² = (30 - 163.5)^2 + (155 - 163.5)^2 + (205 - 163.5)^2+ (235 - 163.5)^2 + (180 - 163.5)^2 + (235 - 163.5)^2 + (70 - 163.5)^2 + (250 - 163.5)^2 + (135 - 163.5)^2 + (145 - 163.5)^2 + (225 - 163.5)^2 + (230 - 163.5)^2 + (30 - 163.5)^2 = 73519.25

Standard deviation = √(73519.25/13) = 75.2

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≤ 150

For the alternative hypothesis,

µ > 150

It is a right tailed test.

a) Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 13,

Degrees of freedom, df = n - 1 = 13 - 1 = 12

t = (x - µ)/(s/√n)

Where

x = sample mean = 163.5

µ = population mean = 150

s = samples standard deviation = 75.2

t = (163.5 - 150)/(75.2/√13) = 0.65

The lower the test statistic value, the higher the p value and the higher the possibility of accepting the null hypothesis.

b) We would determine the p value using the t test calculator. It becomes

p = 0.26

Since alpha, 0.05 < than the p value, 0.26, then we would fail to reject the null hypothesis. Therefore, At a 5% level of significance, the sample data does not show significant evidence that the mean number of friends for the student population at the college who use the social media website is larger than 150.

c)

1.The test statistic value is the difference between the sample mean and the null hypothesis value.

Answer:

L(xyz) = ( 1 , 3 , -7 )

L = x + 3y - 7z -3

Step-by-step explanation:

f (x,y,z) = xy + 2yz - 3xz

f (3,1,0) = (3) (1) + 2 (1) (0) - 3 (3) (0)

f (3,1,0) = 3

fx = y - 3z

f (3,1,0) = (1) - 3 (0)

fx = 1

fy = x + 2z

f (3,1,0) = (3) - 2 (0)

fy = 3

fz = 2y - 3x

f (3,1,0) = 2 (1) - 3 (3)

fz = -7

Answer: The monthly mortgage payment is $640

Step-by-step explanation:

The cost of the house is $159,000

The down payment made is 20%. This means that the amount paid as down payment is

20/100 × 159000 = 31800

The balance to be paid would be

159000 - 31800 = $127200

We would apply the periodic interest rate formula which is expressed as

P = a/[{(1+r)^n]-1}/{r(1+r)^n}]

Where

P represents the monthly payments.

a represents the amount of the loan

r represents the annual rate.

n represents number of monthly payments. Therefore

a = $127200

r = 0.044/12 = 0.0037

n = 12 × 30 = 360

Therefore,

P = 127200/[{(1+0.0037)^360]-1}/{0.0037(1+0.0037)^360}]

P = 127200/[{(1.0037)^360]-1}/{0.0037(1.0037)^360}]

P = 127200/{3.779 -1}/[0.0037(3.779)]

P = 127200/(2.779/0.0139823)

P = 127200/198.75127840198

P = $640

Answer:

3 1/2 gallons or 56 cups

Step-by-step explanation:

1. Analyze the questions.

We have 3 gallons, and we add another 1/2 gallon. This means that our equation must be 3 + 1/2.

2. Solve.

3 + 1/2 = 3 1/2 gallons

3. Convert.

1 gallon = 16 cups

1 * 3 1/2 gallons = 16 * 3 1/2 cups

3 1/2 gallons = 56 cups

Answer: 3 1/2

                           Hope this helped! :D

Answer:

bh

6, 17

102

51

Step-by-step explanation:

Answer:

1/2 (bh)

1/2(17)(6)

51

Answer:

Step-by-step explanation:

If the profit realized by the company is modelled by the equation

P (x) = −0.5x² + 120x + 2000, marginal profit occurs at dP/dx = 0

dP/dx = -x+120

P'(x) = -x+120

Company's marginal profit at the $100,000 advertising level will be expressed as;

P '(100) = -100+120

P'(100) = 20

Marginal profit at the $100,000 advertising level is $20,000

Company's marginal profit at the $140,000 advertising level will be expressed as;

P '(140) = -140+120

P'(140) = -20

Marginal profit at the $140,000 advertising level is $-20,000

Based on the marginal profit at both advertising level, I will recommend the advertising expenditure when profit between $0 and $119 is made. At any marginal profit from $120 and above, it is not advisable for the company to advertise because they will fall into a negative marginal profit which is invariably a loss.

a) The percentage of women meeting the height requirement is approximately 99.99%.

b) The percentage of men meeting the height requirement is approximately 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) To find the percentage of women meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we need to calculate the proportion of women within this range using the normal distribution.

First, we standardize the height requirement using the formula:

Z = (X - μ) / σ

where X is the value (height), μ is the mean, and σ is the standard deviation.

For the lower limit (57 inches):

Z_lower = (57 - 63.3) / 2.7 ≈ -2.33

For the upper limit (76 inches):

Z_upper = (76 - 63.3) / 2.7 ≈ 4.70

Using a standard normal distribution table or calculator, we can find the area between -2.33 and 4.70. This represents the percentage of women meeting the height requirement.

The percentage of women meeting the height requirement is approximately 99.99%.

b) Similarly, for men meeting the height requirement of being between 4ft 9in (57 inches) and 6ft 4in (76 inches), we standardize the values:

For the lower limit (57 inches):

Z_lower = (57 - 67.3) / 2.8 ≈ -3.68

For the upper limit (76 inches):

Z_upper = (76 - 67.3) / 2.8 ≈ 3.11

Using the standard normal distribution table or calculator, we find the area between -3.68 and 3.11.

The percentage of men meeting the height requirement is approximately 99.95%.

c) To find the new height requirements that exclude the tallest 5% of men and the shortest 5% of women, we need to determine the corresponding Z-scores.

For men:

Z_upper_men = Z(0.95) ≈ 1.645

For women:

Z_lower_women = Z(0.05) ≈ -1.645

Using these Z-scores, we can calculate the new height requirements:

For the new lower limit:

X_lower = Z_lower_women * σ + μ

For the new upper limit:

X_upper = Z_upper_men * σ + μ

Substituting the values:

X_lower = -1.645 * 2.7 + 63.3 ≈ 58.53 inches

X_upper = 1.645 * 2.8 + 67.3 ≈ 71.78 inches

Therefore, the new height requirements are at least 58.5 inches and at most 71.8 inches.

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a) The percentage of women meeting the height requirement is 99.99%.

b) The percentage of men meeting the height requirement is 99.95%.

c) The new height requirements are at least 58.5 inches and at most 71.8 inches.

a) For women meeting the height requirement:

Given: Mean (μ) = 63.3 in.

Standard Deviation (σ) = 2.7 in.

So, Minimum height requirement:

= 4 ft 9 in

= 4 * 12 + 9

= 57 inches

and, Maximum height requirement:

= 6 ft 4 in

= 6 * 12 + 4

= 76 inches

We will calculate the Z-scores for these heights using the formula:

Z = (x - μ) / σ

For the minimum height requirement:

[tex]Z_{min[/tex] = (57 - 63.3) / 2.7 ≈ -2.33

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 63.3) / 2.7 ≈ 4.70

So, the the area between -2.33 and 4.70.

Thus, the percentage is  99.99%.

b) For men meeting the height requirement:

Given: Mean (μ) = 67.3 in., Standard Deviation (σ) = 2.8 in.

Minimum height requirement: 4 ft 9 in = 57 inches

Maximum height requirement: 6 ft 4 in = 76 inches

For the minimum height requirement:

[tex]Z_{min[/tex]= (57 - 67.3) / 2.8 ≈ -3.68

For the maximum height requirement:

[tex]Z_{max[/tex] = (76 - 67.3) / 2.8 ≈ 3.11

So, the area between -3.68 and 3.11.

Thus, the percentage is 99.95%.

c) For the new height requirements:

For men:

[tex]Z_{upper_{men[/tex] = Z(0.95) ≈ 1.645

For women:

[tex]Z_{lower_{women[/tex] = Z(0.05) ≈ -1.645

For the new lower limit:

[tex]X_{lower} = Z_{lower}_{women} \sigma+ \mu[/tex]

For the new upper limit:

[tex]X_{upper} = Z_{upper}_{men} \sigma+ \mu[/tex]

Substituting the values:

[tex]X_{lower} = -1.645 * 2.7 + 63.3[/tex]

           = 58.53 inches

and, [tex]X_{upper} = 1.645 * 2.8 + 67.3[/tex]

                     = 71.78 inches

Therefore, the new height at least 58.5 inches and at most 71.8 inches.

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Answer:

5^15

Step-by-step explanation:

(5^10)(5^5)= 5^10+5= 5^15