Answer:
a) We can not estimate the probability.
b) Zero probability.
c) There is a probability between 95% and 99% that they have between 475 and 525 customers on a given day.
Step-by-step explanation:
a) We can not said nothing because we only know the average of customers per day. We need to know the probability distribution of the amount of customers per day to answer this question.
b) Now that we know that the variance is 100, although we do not know the exact distribution of the values, we can use the empirical rules to estimate the probability of having at least 700 customers on a given day.
If the variance is 100, the standard deviation is √100=10.
Applying the empirical rule (68-95-99.7 rule), we know that there is probability 0.15% of having at least 500+3*10=530 customers per day (more than 3 deviations from the mean).
Then, we can conclude that the probability of having at least 700 customers per day is zero.
c) To estimate this probability, we have to calculate how many deviations from the mean this values represent:
[tex]\Delta_1=475-500=-25=2.5\sigma\\\\\Delta_2=525-500=25=2.5\sigma[/tex]
We have an interval that have a width of ±2.5 deviations from the mean.
For 2 deviations from the mean, it is expected to have 95% of the data.
For 3 deviations from the mean, it is expected to have 99.7% of the data.
Then, for the interval 475 to 525, we can estimate a probability between 95% and 99%.
The most common form of color blindness is an inability to distinguish red from green. However, this particular form of color blindness is much more common in men than in women (this is because the genes corresponding to the red and green receptors are located on the X-chromosome). Approximately 79% of American men and 0.4% of American women are red-green color-blind.1 Let CBM and CBW denote the events that a man or a woman is color-blind, respectively.
(a) If an Americal male is selected at random, what is the probability that he is red-green color-blind? P(CBM) =
(b) If an American female is selected at random, what is the probability that she is NOT red-green color-blind? P (not CBW) =
(c) If one man and one woman are selected at random, what is the probability that neither are red-green color-blind? P=(neither is color-blind) =
(d) If one man and one woman are selected at random, what is the probability that at least one of them is red-green color-blind? P=(at least one is color-blind)
Answer:
(a) P(CBM) = 0.07
(b) P(not CBW) = 0.996
(c ) P(neither is color-blind) = 0.926
(d) P=(at least one is color-blind) = 0.074
Step-by-step explanation:
The correct data is that Approximately 7% of American men and 0.4% of American women are red-green color-blind.
(a) Probability that he is red-green color-blind:
[tex]P(CBM) = 0.07[/tex]
(b) Probability that she is NOT red-green color-blind:
[tex]P(not\ CBW) =1- P(CBW)\\P(not\ CBW) = 1 -0.004\\P(not\ CBW) =0.996[/tex]
(c) Probability that neither are red-green color-blind
[tex]P(neither) = P(not\ CBW)*P(not\ CBM) \\P(neither) = 0.996 *(1-0.07)\\P(neither)=0.926[/tex]
(d) Probability that at least one of them is red-green color-blind
[tex]P(at\ least\ one) = 1- P(neither) \\P(at\ least\ one) = 1-0.926\\P(at\ least\ one) = 0.074[/tex]
evaluate...
(2/1) to the power -2
Answer:
hope this helps :)
Step-by-step explanation:
1/4 because 2/1 is 2 and 2 to the power of -2 is 1/4
I need help with this one
Answer:
2 2/3
Step-by-step explanation:
HELP PLEASE!!!!!!!!!!!!!!
Answer:
Savannah
Step-by-step explanation:
Emery has solved it incorrectly;
x = 100
What’s the correct answer for this question?
Answer:
Height = 12 inches
Step-by-step explanation:
Volume = Area × Height
1080 = 90 × H
H = 1080/90
H = 12 inches
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. This problem is an example of a a. Marascuilo procedure. b. multinomial population. c. z test for proportions. d. test for independence.
Answer:
The correct answer will be Option B (multinomial population).
Step-by-step explanation:
The population is considered as multinomial whether its information is prescriptive or corresponds to the set of discreet non-overlapping groups. The hypothesis again for fitness test besides multinomial distribution is that even though the approximately normal f I seem to be equivalent to the required number e I across each segment.Here, because we have been testing whether the sampling data matches the hypothesized proportions as mentioned, this is indeed a multinomial population issue (because there have been more least two generations).Other given options are not connected to the given situation. So that Option B seems to be the perfect solution.
Find the length of both of the unknown sides in the triangle shown here.
Give your answer correct to the nearest metre. [5 marks]
Answer:
[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]
And if we solve this equation for x we got:
[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]
We can cancel [tex]x^2[/tex] in both sides and we have this:
[tex] 22x -6x= 256+9-121 =144[/tex]
And then we got:
[tex] 16 x= 144[/tex]
[tex] x =\frac{144}{16}= 9[/tex]
And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side.
Lenght of the smaller unknown side: 12m
Lenght of the larger unknown side: 20m
Step-by-step explanation:
For this case we have a right triangle and we can use the Pythagoras Theorem and using the info given by the triangle we can set up the following equation:
[tex] (x+11)^2 = (x+3)^2 +16^2[/tex]
And if we solve this equation for x we got:
[tex] x^2 +22x +121 = x^2 +6x +9 +256[/tex]
We can cancel [tex]x^2[/tex] in both sides and we have this:
[tex] 22x -6x= 256+9-121 =144[/tex]
And then we got:
[tex] 16 x= 144[/tex]
[tex] x =\frac{144}{16}= 9[/tex]
And then the length of the sides are 9+11= 20 m for the hypothenuse, 16 for the adjacent side and 9+3 = 12m for the last side side.
Lenght of the smaller unknown side: 12m
Lenght of the larger unknown side: 20m
The fraction of students ages 10 to 17 who favor math or science is
Answer:
So if 17/25 of the students like math, science, and art and 3/20 of the students like art only. We first need to find common demoninator. 68/100 and for the second one 15/100. Subtract them both
68-15 = 53/100 of the students factor math, and science or 53%
Find the x-intercept(s) and the coordinates of the vertex for the parabola.
Answer:
see explanation
Step-by-step explanation:
Given
y = x² - 2x - 8
To find the x- intercepts let y = 0 , that is
x² - 2x - 8 = 0 ← in standard form
(x - 4)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 2 = 0 ⇒ x = - 2
x- intercepts : x = - 2, x = 4
The x- coordinate of the vertex is mid way between the x- intercepts, that is
[tex]x_{vertex}[/tex] = [tex]\frac{-2+4}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1
Substitute x = 1 into the equation for corresponding y- coordinate
y = 1² - 2(1) - 8 = 1 - 2 - 8 = - 9
vertex = (1, - 9 )
One-third times the difference of a number and 5 is
Which equation best shows this?
3
One possible first step in solving the equation in the above problem is to
The value of the number is
Answer:
the value of x is 3
Step-by-step explanation:
Hope this helps!!!! :)
Answer:
one is a
two is c
three is b
Step-by-step explanation:
Solve for x: 3x - 5 = 2x + 6.
Your answer
Answer:
3x-5=2x+6
x-5=6
x=11
Written as a simplified polynomial in standard form, what is the result when
(x + 1)2 is subtracted from 7x2 - 4x + 6?
Answer:
The resultant polynomial is: [tex]6x^2-6x+5[/tex]
Step-by-step explanation:
We need to subtract [tex](x+1)^{2}[/tex] from [tex]7x^2-4x+6[/tex]
so, we start by performing the multiplication involved in the perfect square of the binomial [tex](x+1)[/tex], and obtain its expression in separate terms that can be combined:
[tex](x+1)^{2}=(x+1)\,(x+1)=x^2+x+x+1=x^2+2x+1[/tex]
Now we can subtract this trinomial from [tex]7x^2-4x+6[/tex], and combining like terms to get the resultant polynomial expression:
[tex]7x^2-4x+6-(x^2+2x+1)=7x^2-4x+6-x^2-2x-1=7x^2-x^2-4x-2x+6-1=6x^2-6x+5[/tex]
Then the resultant polynomial is: [tex]6x^2-6x+5[/tex]
Suppose that weekly income of migrant workers doing agricultural labor in Florida has a distribution with a mean of $520 and a standard deviation of $90. A researcher randomly selected a sample of 100 migrant workers. What is the probability that sample mean is less than $510
Answer:
[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]
And we can find the probability using the normal standard distribution table and with the complement rule we got:
[tex]P(z<-1.11)= 0.1335[/tex]
Step-by-step explanation:
For this problem we have the following parameters:
[tex] \mu = 520, \sigma = 90[/tex]
We select a sample size of n =100 and we want to find this probability:
[tex] P(\bar X <510) [/tex]
The distribution for the sample mean using the central limit theorem would be given by:
[tex]\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})[/tex]
And we can solve this problem with the z score formula given by:
[tex] z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score formula we got:
[tex] z=\frac{510-520}{\frac{90}{\sqrt{100}}}= -1.11[/tex]
And we can find the probability using the normal standard distribution table and with the complement rule we got:
[tex]P(z<-1.11)= 0.1335[/tex]
On a piece of paper, graph fx) = 2• (0.5)*. Then determine which answer choice matches the graph you drew.
Answer:
Graph A
Step-by-step explanation:
The common ratio is less than 1, so the graph will be decreasing. The initial value is 2, so the y-intercept will be 2. Graph A fits this criteria.
I hope this helps :))
The graph A is correct.
What is a graph?A diagram (such as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables.
The equation is,
[tex]y=2(0.5)^{x}[/tex]
Plotting the graph, we get,
Option A
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What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
Length × Width = Area
So we'll substitute the Area of the circle having formula, πr²
In △DEF, d = 25 in., e = 28 in., and f = 20 in. Find m∠F. Round your answer to the nearest tenth.
Answer:
∠F ≈ 43.9°
Step-by-step explanation:
The Law of Cosines is used to find an angle when all triangle sides are known.
f² = d² +e² -2de·cos(F)
cos(F) = (d² +e² -f²)/(2de) = (25² +28² -20²)/(2·25·28) = 1009/1400
F = arccos(1009/1400)
F ≈ 43.9°
Point R has coordinates (-5, -7) and point T has coordinates (3,-3).
Which point is located 1/4 of the distance from point R to point T?
Enter x-coordinate of the point here .......
and the y-
coordinate of the point here....
Answer:
(x, y) = (-3, -6)
Step-by-step explanation:
The (x, y) distance from R to T is ...
(Δx, Δy) = T - R = (3, -3) -(-5, -7) = (3 -(-5), -3 -(-7)) = (8, 4)
Then 1/4 of the distance is ...
(Δx, Δy)/4 = (8, 4)/4 = (2, 1)
This is added to the R coordinates to find the desired point:
point = R +(2, 1) = (-5, -7) +(2, 1) = (-5+2, -7+1) = (-3, -6)
The coordinates are ...
x-coordinate: -3
y-coordinate: -6
3. Write 52/6
as a mixed number.
Give your answer in its simplest form.
Answer:
26/3 as an improper fraction in simplest form. :)
Step-by-step explanation:
Which answer choice contains only equations? 2 + h = 14 and k minus 25 = 2 c minus 14 and d + 134 10 = 3 + s and 22 minus y 15 + x and 55 = r minus 1
Answer:
2 + h = 14 and k - 25 = 2
Step-by-step explanation:
An equation has an equal sign.
Apparently, your answer choices are of the form ...
(math expression) and (math expression)
In order for this to be "only equations", each "math expression" must contain an equal sign. That is, you must have ...
( ... = ... ) and ( ... = ... )
Something like ...
c -14 and d +134
contains no equal signs, so has no equations.
It looks like your appropriate choice is ...
2 + h = 14 and k - 25 = 2
Answer:
the answer is a
Step-by-step explanation:
i took the test
:)
note: have a wonderful day!
Liam needs a guitar case. It must be 1.18 m long. Select the case that is suitable? 11.8mm,118cm,1.8m ,11.18mm
Answer:
118 cm
Step-by-step explanation:
1 m = 100 cm
1 m = 1000 mm
1.18 m = 118 cm = 1180 mm
11.8 mm ----> too small
118 cm ----> just right
1.8 m ----> too big
11.18 mm ----> too small
Where the above dimensions are given, the suitable guitar case for Liam would be the one that is 1.8 m long.
How is this so?Since Liam's guitar case needs to be 1.18 m long, we need to select the option that is closest in length without exceeding it.
Among the given options, 11.8 mm and 11.18 mm are too small, and 118 cm is equal to 1.18 m, which exceeds the required length.
Hence , the only suitable option is 1.8 m, which matches Liam's requirement of a guitar case with a length of 1.18 m.
Learn more about dimension at:
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A horizontal line contains points A, C, B. 2 lines extend from point C. A line extends to point E and another line extends to point D. An arc represents angle A C D.
Ray CE is the angle bisector of AngleACD. Which statement about the figure must be true?
mAngleECD = One-halfmAngleECB
mAngleACE = one-halfmAngleACD
AngleACE Is-congruent-to AngleDCB
AngleECDIs-congruent-to AngleACD
Answer:
Option (2).
Step-by-step explanation:
In the figure attached,
A, C and B are the points lying on a straight line.
2 lines EC and DC have been drawn by extending the lines from C to E and D respectively.
Ray CE is the angle bisector of ∠ACD.
That means CE divides ∠ACD in two equal parts.
m∠ACE = m∠DCE
Since m∠ACD = m∠ACE + m∠DCE
= 2(m∠ACE)
m∠ACE = [tex]\frac{1}{2}(\angle ACD)[/tex]
Therefore, option (2) will be the answer.
Answer:
b
Step-by-step explanation:
took test
A trash company is designing an open-top, rectangular container that will have a volume of 1715 ft cubed. The cost of making the bottom of the container is $5 per square foot, and the cost of the sides is $4 per square foot. Find the dimensions of the container that will minimize total cost.
Answer:
14 ft × 14 ft × 8.75 ft
Step-by-step explanation:
A garbage company is designing an open rectangular container that should have a volume of 1,715 cubic feet.
So we have the length of the container = "x" ft, the width of the container = "y" ft and the height of the container = "z" ft
Therefore the volume of the rectangular container would be:
x * y * z = 1715 ft³
z = 1715 / x * y
The cost of making the bottom of the container is $ 5 per square foot, that is:
5 * (x * y)
Now, area of all sides of the container would be:
2 * (x * z + y * z) = 2 * z * (x + y)
We know that it has been given that the cost of making all the sides of the container is = $ 4 per square foot, so:
4 * (2 * z * (x + y)) = 8 * z * (x + y)
In total the costs would be:
5 * (x * y) + 8 * z * (x + y)
If we replace z, in the previous equation we have:
5 * (x * y) + 8 * (1715 / x * y) * (x + y)
solving, and we would have that the total cost would be:
C = 5 * (x * y) + 13720 / x + 13720 / y
Now we will find the derivative of C and make it equal to zero:
dC / dx = 0; dC / dy = 0
For dC / dx = 0:
dC / dx = 5 * y + 13720 * -1 / (y ^ 2) + 13720 * 0
0 = 5 * y - 13720 / y ^ 2
5 * y = 13720 / y ^ 2
y ^ 3 = 13720/5 = 2744
y = 14
For dC / dy = 0:
dC / dy = 5 * x + 13720 * 0 + 13720 * -1 / (x ^ 2)
0 = 5 * x - 13720 / x ^ 2
5 * x = 13720 / x ^ 2
x ^ 3 = 13720/5 = 2744
x = 14
now for z:
z = 1715 / (14 * 14)
z = 8.75
Therefore, the dimensions of the container should be 14 ft × 14 ft × 8.75 ft to minimize manufacturing cost.
A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 41% of the cameras sold have been of the basic model. Of those buying the basic model, 31% purchase an extended warranty, whereas 48% of all deluxe purchasers do so. If you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model
Answer:
[tex]75.6\%[/tex]
Step-by-step explanation:
Let B be the event of buying a basic model.
Given that P(B) = 41%
Let D be the event of buying a basic model.
Given that P(D) = 1 - 41% = 59%
Let E be the event of extended warranty.
Given that:
P(E [tex]\cap[/tex] B) = 31% and
P(E [tex]\cap[/tex] D) = 48%
P(E) = P(E [tex]\cap[/tex] B) [tex]\times[/tex] P(B) + P(E [tex]\cap[/tex] D) [tex]\times[/tex] P(D)
P(E) = 31% [tex]\times[/tex] 41% + 48% [tex]\times[/tex] 59% = 0.4103
To find: P(B/E)
Formula:
[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]
[tex]\Rightarrow \dfrac{0.31}{0.41}\\\Rightarrow 0.756\\\Rightarrow 75.6\%[/tex]
So, the correct answer is [tex]75.6\%[/tex].
Here is rectangle A. Block A. Rectangle B is ¹/₅ longer than A Block B. Rectangle C is ¹/₃ longer than B Block C. The total length of all three rectangles is 133 cm. How much longer is rectangle C than B?
Answer:
Rectangle C is 14 cm longer than B
Step-by-step explanation:
Let x be the length of Rectangle A. Rectangle B is ¹/₅ longer than A Block B,
Therefore the length of rectangle B is:
[tex]x+\frac{1}{5}x[/tex]
Rectangle C is ¹/₃ longer than B, therefore the length of rectangle c is:
[tex]x+\frac{1}{5}x+\frac{1}{3}(x+\frac{1}{5}x) =x+ \frac{1}{5}x+\frac{1}{3}x+\frac{1}{15}x=x+\frac{9}{15}x[/tex]
The total length of all three rectangles is 133 cm.
Length of rectangle A + Length of rectangle B + Length of rectangle C = 133 cm
[tex]x+x+\frac{1}{5}x +x+\frac{9}{15}x=133\\x+x+x+\frac{1}{5}x +\frac{9}{15}x=133\\3x+\frac{12}{15}x=133\\ 45x+12x=1995\\57x=1995\\x=35cm[/tex]
Therefore the length of rectangle A is 35 cm, the length of rectangle B is [tex]35+\frac{1}{5}*35=42\ cm[/tex] and the length of rectangle C is [tex]35+\frac{9}{15}*35=56\ cm[/tex]
Rectangle C is ¹/₃ longer than B, which is 14 cm (42\3) longer than B
Company A makes a large shipment to Company B. Company B can reject the shipment if they can conclude that the proportion of defective items in the shipment is larger than 0.1. In a sample of 400 items from the shipment, Company B finds that 59 are defective. Conduct the appropriate hypothesis test for Company B using a 0.05 level of significance.
Answer:
[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]
The p value for this case would be given by:
[tex]p_v =P(z>3.17)=0.00076[/tex]
For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment
Step-by-step explanation:
Information provided
n=400 represent the random sample taken
X=59 represent number of defectives from the company B
[tex]\hat p=\frac{59}{400}=0.1475[/tex] estimated proportion of defectives from the company B
[tex]p_o=0.1[/tex] is the value to verify
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true proportion of defectives is higher than 0.1 then the system of hypothesis are.:
Null hypothesis:[tex]p \leq 0.1[/tex]
Alternative hypothesis:[tex]p > 0.1[/tex]
The statistic would be given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing the info given we got:
[tex]z=\frac{0.1475-0.1}{\sqrt{\frac{0.1(1-0.1)}{400}}}=3.17[/tex]
The p value for this case would be given by:
[tex]p_v =P(z>3.17)=0.00076[/tex]
For this case the p value is lower than the significance level so then we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly higher than 0.1 and then Company B can reject the shipment
Which graph shows exponential growth?
The answer is graph A 7/9/20 edge
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
Assume that 1100 births are randomly selected and exactly 556 of the births are girls. Use subjective judgment to determine whether the given outcome is unlikely, and also determine whether it is unusual in the sense that the result is far from what is typically expected.
Answer:
The sample proportion for the births that are girls is 0.505. It is slightly higher than the expected value of 0.5, but the right way to answer if it is an unusual proportion is by performing an hypothesis test.
The hypothesis test results in not enough evidence to claim that the outcome is unlikely. This sample result has a probability of 0.7627 of appearing by pure chance in a population with proportion p=0.5.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the proportion of girls birth differs significantly from the expected proportion (50%).
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi\neq 0.5[/tex]
The significance level is 0.05.
The sample has a size n=1100.
The sample proportion is p=0.505.
p=X/n=556/1100=0.505
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{1100}}\\\\\\ \sigma_p=\sqrt{0.000227}=0.015[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.505-0.5-0.5/1100}{0.015}=\dfrac{0.005}{0.015}=0.302[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=2\cdot P(z>0.302)=0.7627[/tex]
As the P-value (0.7627) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the proportion of girls birth differs significantly from the expected proportion (50%).
Need help ASAP please!!
Answer:
AOB = 73
BOC = 107
Step-by-step explanation:
So make an equation.
9x + 27 = 180
9x = 153
x = 17
AOB = 73
BOC = 107
A diagonal of a cube measures 30 inches. The diagonal of a face measures StartRoot 600 EndRoot inches.
In inches, what is the length of an edge of the cube? Round the answer to the nearest tenth.
Answer:
17.3 Inches
Step-by-step explanation:
Given that the diagonal of a cube = 30 inches
For a cube of side length s, Length of its diagonal [tex]=s\sqrt{3}[/tex]
Therefore:
[tex]s\sqrt{3}=30\\$Divide both sides by \sqrt{3}\\s=30 \div \sqrt{3}\\s=17.3$ inches (to the nearest tenth.)[/tex]
Side Length of the cube is 17.3 Inches.
Answer:
17.3
Step-by-step explanation:
Edge 2020
A research scientist wants to know how many times per hour a certain strand of bacteria reproduces. The mean is found to be 7.8 reproductions and the population standard deviation is known to be 2.2. If a sample of 697 was used for the study, construct the 85% confidence interval for the true mean number of reproductions per hour for the bacteria. Round your answers to one decimal place.
Answer:
The 85% confidence interval is ( 7.7 , 8.0 )
Step-by-step explanation:
In order to find the 85% confidence interval you use the following formula:
[tex]\overline{x}\pm Z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
where
[tex]\overline{x}[/tex]: mean of number of bacteria reproduces per hour = 7.8
σ: standard deviation = 2.2
n: sample size = 967
α: 1 - 0.85 = 0.15
Zα/2: Z factor of the density distribution = 1.44
You replace the values of all parameters in the equation (1):
[tex]7.8\pm (1.44)\frac{2.2}{\sqrt{697}}\\\\7.8\pm0.119\\\\[/tex]
Then, the confidence interval is:
[tex](7.8-0.119,7.8+0.119)\\\\(7.7,8.0)[/tex]