Question

Suppose a simple random sample of size n=200 is obtained from a population whose size is N=10,000 and whose population proportion with a specified characteristic is p=0.6.

Complete parts **(a)** through**
(c)** below**.**

**(a)** Describe the sampling distribution of
ModifyingAbove p with caretp.

Determine the mean of the sampling distribution of ModifyingAbove p with caretp.

mu Subscript ModifyingAbove p with caret equals

μp=___

(Round to one decimal place as needed.)

Determine the standard deviation of the sampling distribution of

sigma Subscript ModifyingAbove p with caret

σp=___

(Round to six decimal places as needed.)

**(b)** What is the probability of obtaining x=128
or more individuals with the characteristic? That is, what is
P(p^≥0.64)?

P(p^≥0.64)=___

(Round to four decimal places as needed.)

**(c)** What is the probability of obtaining x=106
or fewer individuals with the characteristic? That is, what is
P(p^≤0.53)?

P(p^≤0.53)=___

(Round to four decimal places as needed.)

Answer #1

a) np(1 - p) = 200 * 0.6 * (1 - 0.6) = 48

As np(1 - p) > 10, so the sampling distribution of will be approximately normally distributed.

= 0.6

= 0.034641

b) P( > 0.64)

= P(Z > 1.15)

= 1 - P(Z < 1.15)

= 1 - 0.8749

= 0.1251

c)

P( < 0.64)

= P(Z < -2.02)

= 0.0217

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