Question

the population proportion is .7 and the sample size is large , what is the probability that the sample proportion is less than .6 ?

Answer 1

Sol:-

Since the sample size is large, the sample proportion should converge towards the population proportion.

Hence, for the sample

And standard deviation

We don't know the value of n, so we would take it as 100, which is a good minimum estimate for a large sample size to get accurate results.

Now

(using the z-table)

Hence the required probability that the sample proportion is less than 0.6 = 0.015

Thank you!!

Please upvote!!