Question

2. A university administrator expects that 30% of students in a core course will receive an A. He looks at the grades assigned to 100 students. The probability that the proportion of students that receive an A is 0.25 or less is ________.

Answer 1

The probability that the proportion of students that receive an A is 0.25 or less is = 0.1379

Explanation:

Given -

A university administrator expects that 30% of students in a core course will receive an A.

Sampling distribution of sample proportion
`(\\u _\widehat{p})` = p = 30% = 0.30

Sample size ( n ) = 100

Standard deviation of sample proportion
`(\sigma _\widehat{p})` =
`\sigma _{\widehat{p}} = \sqrt{(p (1 - p))/(n)}` =
`\sqrt{((0.30) (0.70))/(100)}` = .0458

The probability that the proportion of students that receive an A is 0.25 or less is =
`P(\widehat{p} \leq 0.25)`

=
`P(\frac{\widehat{p} - \\u _{\widehat{p}}}{\sigma _{\widehat{p}}}\leq (0.25 - 0.30)/(.0458) )` Putting
`(Z = \frac{\widehat{p} - \\u _{\widehat{p}}}{\sigma_{\widehat{p}}} )`

=
`P(Z \leq -1.09)` Using Z table

= 0.1379