Question

A university administrator expects that 25% of students in a core course will receive an

a. he looks at the grades assigned to 60 students. the probability that the proportion of students that receive an a is 0.20 or less is ________.

Answer 1

75% i would think if you subtract 25% from 100% of the class

Answer 2

18.67% probability that the proportion of students that receive an a is 0.20 or less.

Explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (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.

In this problem, we have that:

`\mu = 0.25`.

The standard deviation of a proportion
`\pi` is given by the following formula.

`\sigma = \sqrt{(\pi(1-\pi))/(n)}`

A university administrator expects that 25% of students in a core course will receive an a. There are 60 students. So
`\pi = 0.25, n = 60` and
`\sigma = \sqrt{(0.25*(0.75))/(60)} = 0.0559`

The probability that the proportion of students that receive an a is 0.20 or less is

This is the pvalue of Z when X = 0.2. So

`Z = (X - \mu)/(\sigma)`

`Z = (0.2 - 0.25)/(0.0559)`

`Z = -0.89`

`Z = -0.89` has a pvalue of 0.1867.

So there is an 18.67% probability that the proportion of students that receive an a is 0.20 or less.