Question

g Suppose 40% of the students in a university are baseball players. If a sample of 781 students is selected, what is the probability that the sample proportion of baseball players will be greater than 43%

Answer 1

Answer: 0.1271

Explanation:

Let p= probability of the students in a university are baseball players.

Given: p= 0.40 , sample size : n= 781

The probability that the sample proportion of baseball players will be greater than 43% will be:

`P(p>0.43)=P(\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}>\frac{0.43-0.41}{\sqrt{(0.41(1-0.41))/(781)}}\\\\=P(Z>1.14)\ \ \ [Z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}]\\\\=1-P(Z<1.14)\\\\=1- 0.8729=0.1271`

Hence, the probability that the sample proportion of baseball players will be greater than 43% = 0.1271