Question

In: Statistics and Probability

Given that the population proportion is 0.6, a sample of size 1200 is drawn from the...

Given that the population proportion is 0.6, a sample of size 1200 is drawn from the population.

(a) Find the mean and variance of the sampling distribution of sample proportion.
(b) Find the probability that the sample proportion is less than 0.58.
(c) If the probability that the sample proportion is greater than k is 0.6, find the value of k.

Solutions

Expert Solution

(a)

Here, we have,

n = 1200

p = 0.6

Mean of sampling distribution of sample proportion = = 0.6

Variance of sampling distribution of sample proportion :

(b)

Probability that sample proportion is less than 0.58 = P(p<0.58)

We use Excel function "NORMSDIST()" as :

So,

Probability that sample proportion is less than 0.58 = 0.079

(c)

We need to find k such :

We use Excel function "NORMSINV()"as :

orchestra answered 1 year ago

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