Question

Suppose a simple random sample of size n=200 is obtained from a population whose size is N = 30,000 and whose population proportion with a specified characteristic is p=0.4. Complete parts (a) through (c) below. Click Here for StatCrunch (a) Describe the sampling distribution of P. Determine the mean of the sampling distribution of . Hq (Round to one decimal place as needed.) Determine the standard deviation of the sampling distribution of p. 0.- (Round to six decimal places as needed.) (b) What is the probability of obtaining x = 90 or more individuals with the characteristic? That is what is PO 20.45)? PÔ20.45)=(Round to four decimal places as needed.) (c) What is the probability of obtaining x = 64 or fewer individuals with the characteristic? That is what is P S 0.32)? P 0.32)=(Round to four decimal places as needed.)

Answer 1

Ans a) Sampling Distribution is approximately normal because $n\leq0.05N$ and

np(1-p) > 10

Mean of sampling distribution:

$\mu_{\hat{p}} = 0.4$ ans.

The standard deviation of sampling distribution:

p(1-P) 6

¥0.4(1 -0.4) 200

$=0.034641$ ans.

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Ans b)

$P(\hat{p}\geq0.45) = 1 - P(z \leq \frac{0.45-0.4}{0.034641})$

$= 1 - P(z \leq 1.44)$

ans,

/* We can find probability using excel function: =NORM.S.DIST(1.44,TRUE)*/

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Ans c)

$P(\hat{p}\leq0.32) = P(z \leq \frac{0.32-0.4}{0.034641})$

$= P(z \leq -2.31)$

ans.

/* PLEASE UPVOTE */