Question

The mean quantitative score on a standardized test for female​ college-bound high school seniors was 550...

The mean quantitative score on a standardized test for female​ college-bound high school seniors was

550

The scores are approximately Normally distributed with a population standard deviation of

50

A scholarship committee wants to give awards to​ college-bound women who score at the

96TH

percentile or above on the test. What score does an applicant​ need? Complete parts​ (a) through​ (g) below.The mean quantitative score on a standardized test for female​ college-bound high school seniors was

550

The scores are approximately Normally distributed with a population standard deviation of

50

A scholarship committee wants to give awards to​ college-bound women who score at the

96

percentile or above on the test. What score does an applicant​ need? Complete parts​ (a) through​ (g) below.

A.

The 96th percentile has 96​% of the area to the left because it is higher than 96​% of the scores. The table above gives the areas to the left of​ z-scores. Therefore, we look for 0.9600 in the interior part of the table. Use the Normal table given above to locate the area closest to 0.9600. Then report the​ z-score for that area.

Homework Answers

Answer #1

Solution:-

Given that,

mean = = 550

standard deviation = = 50

Using standard normal table,

P(Z > z) = 96%

= 1 - P(Z < z) = 0.96  

= P(Z < z) = 1 - 0.96

= P(Z < z ) = 0.04

= P(Z < -1.75 ) = 0.04  

z = -1.75

Using z-score formula,

x = z * +

x = -1.75 * 50 + 550

x = 462.5

test score = 463

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
One year, many college-bound high school seniors in the U.S. took the Scholastic Aptitude Test (SAT)....
One year, many college-bound high school seniors in the U.S. took the Scholastic Aptitude Test (SAT). For the verbal portion of this test, the mean was 425 and the standard deviation was 110. Based on this information: a) What proportion scored 500 or above? Draw the picture! b) What proportion of the students would be expected to score between 350 and 550? Draw the picture.
One year, many college-bound high school seniors in the U.S. took the Scholastic Aptitude Test (SAT)....
One year, many college-bound high school seniors in the U.S. took the Scholastic Aptitude Test (SAT). For the verbal portion of this test, the mean was 425 and the standard deviation was 110. Based on this information: a) What proportion scored 500 or above? Draw the picture! b) What proportion of the students would be expected to score between 350 and 550? Draw the picture. Type Everything Please
Test C is a standardized test that all high school seniors take. In an SRS of...
Test C is a standardized test that all high school seniors take. In an SRS of 28 seniors, the sample standard deviation is 16. A high school counselor hypothesizes that the mean score on Test C for all high school seniors is 59. Here are the null and alternative hypotheses: H0 : µ = 59 H1 : µ not equal to 59 (a) How far (in points) above/below 59 would the sample mean have to be to reject the null...
A random sample of 12 high school seniors took a standardized mathematics test and made scores:...
A random sample of 12 high school seniors took a standardized mathematics test and made scores: 78, 78, 65, 77, 65, 81, 83, 59, 76, 75, 83, 59 Past scores at the same high school have been Normally distributed with LaTeX: \sigma σ =9.3 Is this sample evidence at the α =0.01 level that the average test score for all students is less than 75? State the hypotheses and calculate a test statistic and P-value in order to answer the...
A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure...
A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless examine the relationship between scores on this test and performance in college. We have chosen a random sample of fifteen students just finishing their first year of college, and for each student we've recorded her score on this standardized test (from 400 to 1600 ) and her grade point average (from 0 to 4 ) for her first...
According to the College Board, the mean score in 2017 for the Scholastic Aptitude Test (SAT)...
According to the College Board, the mean score in 2017 for the Scholastic Aptitude Test (SAT) was 1060 points with a standard deviation of 195 points https://collegereadiness.collegeboard.org/pdf/sat‐percentile‐ranks‐gender‐race‐ ethnicity.pdf). Assume that SAT scores are normally distributed. A. Approximately what percent of SAT‐takers score between 800 and 1200? B. Approximately what percent of SAT‐takers score 1340 and above? C. Approximately what is the probability of a random sample of 9 SAT‐ takers getting a group average score of 1340 and above? Is...
You are asked to do a study of shelters for abused and battered women to determine...
You are asked to do a study of shelters for abused and battered women to determine the necessary capacity I your city to provide housing for most of these women. After recording data for a whole year, you find that the mean number of women in shelters each night is 250 , with a standard deviation of 75 . Fortunately, the distribution of the number of women in the shelters each night is normal, so you can answer the following...