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