A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift the focus from what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded was modified, with the total score of the four sections on the test ranging from 472 to 528. In spring 2015, the mean score was 500.0 with a standard deviation of 10.6.

Required:
What are the median and the first and third quartiles of the MCAT scores?

Answer:

The median of the MCAT scores was of 500.

The first quartile of MCAT scores was of 492.845.

The third quartile of MCAT scores was of 507.155.

Step-by-step explanation:

When the distribution is normal, we use 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.

The mean score was 500.0 with a standard deviation of 10.6.

This means that [tex]\mu = 500, \sigma = 10.6[/tex]

Median:

In a normal distribution, the median is the same as the mean, so the median of the MCAT scores was of 500.

First quartile:

This is the 100*(1/4) = 25th percentile, which is X when Z has a pvalue of 0.25. So X when Z = -0.675.

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

[tex]-0.675 = \frac{X - 500}{10.6}[/tex]

[tex]X - 500 = -0.675*10.6[/tex]

[tex]X = 492.845[/tex]

The first quartile of MCAT scores was of 492.845.

Third quartile:

This is the 100*(3/4) = 75th percentile, which is X when Z has a pvalue of 0.75. So X when Z = 0.675.

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

[tex]0.675 = \frac{X - 500}{10.6}[/tex]

[tex]X - 500 = 0.675*10.6[/tex]

[tex]X = 507.155[/tex]

The third quartile of MCAT scores was of 507.155.

The following function is probability Distribution function.
F(x)=6x+1/25, x=0, 1, 2, 3, 4.
Determine the mean, μ, and variance, σ2, of the random variable. Round your answers to two decimal places.

At the beginning of spring, Arun planted a small sunflower in his backyard. When it
was first planted, the sunflower was 15 inches tall. The sunflower then began to grow
at a rate of 1.5 inches per week. How tall would the sunflower be after 3 weeks? How
tall would the sunflower be after w weeks?
Height after 3 weeks:
Height after w weeks:
Submit Answer

what is the correct order of the numbers from least to greatest. 1/2, 0.6, 6%, 6/5​

The width of a rectangle is the length minus 3 units.The area of the rectangle is 10 units. What is the width, in units, of the rectangle?

PLA HELP NEEDED ASAP I WILL GIVE BRAINLESS TO CORRECT ANSWER PLS HELP

Which graph represents the solution set of the inequality Negative 14.5 less-than x?
A number line going from negative 15 to negative 11. An open circle is at negative 13.5. Everything to the right of the circle is shaded.
A number line going from negative 15 to negative 11. A closed circle is at negative 14. Everything to the right of the circle is shaded.
A number line going from negative 15 to negative 11. An open circle is at negative 14.5. Everything to the right of the circle is shaded.
A number line going from negative 15 to negative 11. A closed circle is at negative 15. Everything to the right of the circle is shaded.

Numbers A set of 25 two digit numbers are listed below.
10 17 20 23 24 28 32 39 42 45 46 52 55
58 61 65 66 72 75 78 79 85 94 97 98

Choose one of these numbers at random. Find the probability of the following results.

The sum of the number's digits is odd??

11. A spinner is divided into 12 equal sections. Five of the sections are labeled with
Even numbers, three sections are labeled with vowels, and four of the sections are
labeled with odd numbers. What is the probability of spinning an odd number? Writeyour answer as a fraction fully reduced.

12. You are choosing an outfit. You can choose from blue jeans, black joans or joggers (3 cholcos).
You can choose from a white tee shirt, Orange too shirt, or gray sweatshirt (3 choices). Finally, you
can choose from your Vans or Crocs (2 choices)

a. A tree diagram would have how many branches? (so how many total choices would there be if
you mutipan 18 choices

b. The counting principal would look like what?
Write your answer like a xbxcxd with you putting in numbers for the letters

c. How many different ways can she choose to write the outfit ?

d. What is the probability that you will choose the joggers, orange tee shirt and Croos? Write your answer as a fraction: a/b with a and being numbers?

Lydia invested $8,300 in an account paying an interest rate of 2.2% compounded
daily. Assuming no deposits or withdrawals are made, how long would it take, to the
nearest tenth of a year, for the value of the account to reach $12,690?

Smith and his friends are gaming online on a popular website. An hour later, 6 friends go offline. Five of them continue playing. How many of them were gaming online initially?

WILL MARK BRAINLIEST!!

solve for all values of x.
pls show some work (not all is necessary, but appreciated)

if both problems are done, i’ll mark you the brainliest:)
and i hope you have an amazing day

3
gina practica
3/4
de hora de aeróbicos y
hora de máquinas en el gimnasio; si ella va a
gimnasio solamente los domingos durante un mes, ¿cuántas horas dedica a ejercitarse?​

What percent is 45 of 72?

How do write an equation in slope intercept form

Gabriel contributes 19% of the total cost of bis health care coverage. He pays $38.80 every week towards this contribution. How much does his employer contribute to his health care coverage for the year?​

Write three equivalent fractions for 4/5

A line passes through the point (-8, 6) and has a slope of
5
Write an equation in slope-intercept form for this line.

Which expression is equivalent to d
6d – 3d?

Helpppp need it fast plz

please help PLEASE help​

A farm is to be built in the shape of Quadrilateral ABCD, as shown below. All four sides are equal.

A rhombus ABCD is shown with diagonal AC equal to 12.6 feet and diagonal BD equal to 10.4 feet.

What is the area of the farm? (1 point)

Two sailboats and their triangular sails are shown in the image below.
The top angles of the two sails are congruent. Based on the information in the image, what is the height of the smaller sail
10.1
11.025
5.9
6.4

I NEED HELP!!!... WHATS THE ANWSER FOR THIS??

plz help me really really fast this is my last question to work on

Need help on math question 20 points and brainlest

AHHH HELP
An aquarium holds 11.94 cubic feet of water, and 2.6 feet long and 1.4 feet wide. What is its depth? Round your answer to the nearest whole number.

i’m stuck please help me

The selling prices on
distributed with a mean of $221,000 and a standard deviation of $30,000.

Diego has 48 chocolate chip cookies, 64 vanilla cookies, and 100 raisin cookies for a bake sale. He wants to make the greatest number of bags that have all three cookie flavors and the same number of each flavor per bag. How many bags can he make without having any cookies left over? How many vanilla cookies will be in each bag?

Help Me :^

What is the quotient?

~Negative StartFraction 3 over 8 EndFraction divided by negative one-fourth~

a. Negative 1 and one-half

b. Negative StartFraction 3 over 32 EndFraction

c. StartFraction 3 over 32 EndFraction

d. 1 and one-half