Suppose that 32% of all users the Infinity Affinity Web site drink diet soft drinks regularly

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Question:

Suppose that 32% of all users the Infinity Affinity Web site drink diet soft drinks regularly. What is the probability that in survey of a randomly selected sample of 200 of the site’s users, the proportion who say that they drink diet soft drinks regularly will be 40% or less? (Show your work. As part of your answer, you should confirm that the sampling distribution of p is approximately Normal.)

We are given that: 32% of all users of the Infinity Affinity web site drink diet soft drinks regularly.

i.e. population proportion all users of the Infinity Affinity web site drink diet soft drinks regularly.

Thus,  p = 0.32.

We have random sample of size n = 200.

We have to find: probability that proportion who say they drink diet soft drinks regularly is 40% or less

P(\hat{p} \leq 0.40)=..........?