1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Oksanka [162]
2 years ago
5

A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift the focus fro

m 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?
Mathematics
1 answer:
katrin [286]2 years ago
6 0

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 \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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 \mu = 500, \sigma = 10.6

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.

Z = \frac{X - \mu}{\sigma}

-0.675 = \frac{X - 500}{10.6}

X - 500 = -0.675*10.6

X = 492.845

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.

Z = \frac{X - \mu}{\sigma}

0.675 = \frac{X - 500}{10.6}

X - 500 = 0.675*10.6

X = 507.155

The third quartile of MCAT scores was of 507.155.

You might be interested in
A regulation baseball field measures 90 feet between each base. What is the distance around the bases in yards
professor190 [17]
The distance between each base is 30 yards since 90*(1/3) = 90/3 = 30
In other words, 90 feet is equivalent to 30 yards (3 ft per 1 yard)

The total distance around the bases is 30*4 = 120 yards. This is the perimeter.
5 0
3 years ago
Which of the following is 7/18 closest to? <br> 1/2<br> 0<br> 1
icang [17]
1/2 I think is the answer
3 0
3 years ago
Read 2 more answers
Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there
astraxan [27]
<span>the relationship is that they both have an x that substitutes for them</span>
7 0
3 years ago
In tests of a computer component, it is found that the mean time between failures is 937 hours. A modification is made which is
VladimirAG [237]

Answer:

Null hypothesis is \mathbf {H_o: \mu > 937}

Alternative hypothesis is \mathbf {H_a: \mu < 937}

Test Statistics z = 2.65

CONCLUSION:

Since test statistics is greater than  critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

P- value = 0.004025

Step-by-step explanation:

Given that:

Mean \overline x = 960 hours

Sample size n = 36

Mean population \mu = 937

Standard deviation \sigma = 52

Given that the mean  time between failures is 937 hours. The objective is to determine if the mean time between failures is greater than 937 hours

Null hypothesis is \mathbf {H_o: \mu > 937}

Alternative hypothesis is \mathbf {H_a: \mu < 937}

Degree of freedom = n-1

Degree of freedom = 36-1

Degree of freedom = 35

The level of significance ∝ = 0.01

SInce the degree of freedom is 35 and the level of significance ∝ = 0.01;

from t-table t(0.99,35), the critical value = 2.438

The test statistics is :

Z = \dfrac{\overline x - \mu }{\dfrac{\sigma}{\sqrt{n}}}

Z = \dfrac{960-937 }{\dfrac{52}{\sqrt{36}}}

Z = \dfrac{23}{8.66}

Z = 2.65

The decision rule is to reject null hypothesis   if  test statistics is greater than  critical value.

CONCLUSION:

Since test statistics is greater than  critical value; we reject the null hypothesis. Thus, there is sufficient evidence to support the claim that the modified components have a longer mean time between failures.

The P-value can be calculated as follows:

find P(z < - 2.65) from normal distribution tables

= 1 - P (z ≤ 2.65)

= 1 - 0.995975     (using the Excel Function: =NORMDIST(z))

= 0.004025

6 0
3 years ago
What is this answer 2000(0.085)
grigory [225]
The answer is
2000 x 0.085 = 170
3 0
3 years ago
Other questions:
  • What is the standard deviation of company r's earnings per month for this year? (1) the standard deviation of company r's earnin
    8·1 answer
  • Find the distance between (3,-6)<br> and (2,-4).<br> please help
    10·1 answer
  • Time to test brainly's mathmaticians
    9·1 answer
  • There were 15 students who brought an item for show-and-tell. Each student had 3 minutes to present their item. Write an equatio
    15·1 answer
  • Is 9(3r-4) and 27r- 36 equivalent
    15·2 answers
  • SAVINGS ACCOUNT How much interest will Hannah earn in 4 years if she deposits $630 in a savings account at 6.5% simple interest?
    6·1 answer
  • PLEASE HELP AND ASAP!!!!<br> Find the mean of the given set of numbers. 1, 4, 2, 2, 6, 9
    6·2 answers
  • PLEASE HELP!
    5·2 answers
  • The formula 
    14·1 answer
  • If DH = (4x + 10) in. and HI = (2x − 4) in., then x =_______ , HI =_______ , and ID = _________
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!