Answer:
The probability that the proportion of students that receive an A is 0.25 or less is = 0.1379
Step-by-step explanation:
Given -
A university administrator expects that 30% of students in a core course will receive an A.
Sampling distribution of sample proportion [tex](\nu _\widehat{p})[/tex] = p = 30% = 0.30
Sample size ( n ) = 100
Standard deviation of sample proportion [tex](\sigma _\widehat{p})[/tex] = [tex]\sigma _{\widehat{p}} = \sqrt{\frac{p (1 - p)}{n}}[/tex] = [tex]\sqrt{\frac{(0.30) (0.70)}{100}}[/tex] = .0458
The probability that the proportion of students that receive an A is 0.25 or less is = [tex]P(\widehat{p} \leq 0.25)[/tex]
= [tex]P(\frac{\widehat{p} - \nu _{\widehat{p}}}{\sigma _{\widehat{p}}}\leq \frac{0.25 - 0.30}{.0458} )[/tex] Putting [tex](Z = \frac{\widehat{p} - \nu _{\widehat{p}}}{\sigma_{\widehat{p}}} )[/tex]
= [tex]P(Z \leq -1.09)[/tex] Using Z table
= 0.1379
