Canterville College uses a multiple choice placement test to determine the mathe

Question

Canterville College uses a multiple choice placement test to determine the mathematical skills of an applicant. There is a total of 270 points on the test. The testing companies provides the following table of percentiles: (A) What is the 60th percentile? (B) Suppose the university decides to require that students who score 50 is or less must complete remedial work. True or False: The expectation is that at least 20% of applicants will need to do remedial work. (C) Suppose the university decides to require that students who score 50 or less must complete remedial work. True or False: The expectation is that at least 114 of applicants will need to do remedial work. (D) True or False: Each of the scores in the top 10% are expected to be 260 or higher. (E) True or False: The 35-th percentile must be strictly greater than 105. Suppose that x_1, , x_50 is a list of numbers such that sigma^50_i = 1 x_i = 650 and sigma^50_i = 1 x^2_i = 9411. Also, define a second list by y_i = 5x_i - 11 (A) What is the mean of the x-list? (B) What is the sample standard deviation of the x-list? (C) What is the mean of the y-list? (D) What is the sample standard deviation of the y-list?

Explanation / Answer

Solution:-

1)

A) The 60th percentile is 196.

B) True

The score for the 20th percentile is 45, so atleast 20% of the applicants need to do remedial work.

C) False, Beacuse for the score 50 or less we have atleast 20% of the applicants need to do remedial work.

D) True, 90th percentile is 260, so each score in top 10% would be greater than the 260.

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