Question

I have a sample question that I need help on.
Suppose 48% of the students in a university are baseball players.
If a sample of 427 students is selected, what is the probability that the sample proportion of baseball players will be greater than 44%?

Answer 1

I need an answer quick please its a test.

Answer 2

I came up with 18.18 <z<-18.18

Answer 3

this can be solved with the normal approximation to the binomial distribution, where:
\[mean=np=427\times 0.48=204.96\]
\[\sigma=\sqrt{np(1-p)}=10.324\]
44% of 427 = 187.88
Now you need to calculate the z-score for 187.88 and use a standard normal distribution table.

Answer 4

how would you calculate the zscore for that? i know the formula but not what numbers to plug in

Answer 5

\[z=\frac{X-\mu}{\sigma}\]
X = 187.88
mu = 206.96
sigma = 10.324

Answer 6

thank you so much @kropot72

Answer 7

You're welcome :)