12. Suppose a simple random sample of size n=1000 is obtained from a population

Question

12. Suppose a simple random sample of size n=1000 is obtained from a population whose size is N= 1,500,000 and whose population proportion with a specified characteristic is p=0.44. Complete parts (a) through (c) below.

(a) Describe the sampling distribution of ^p.

MULTIPLE CHOICE

a. Approximately normal, u^p = 0.44 and ^p = 0.0002

b. Approximately normal, u^p = 0.44 and ^p = 0.0157

c. Approximately normal; u^p = 0.44 and ^p = 0.0004

(b) What is the probability of obtaining x=470 or more individuals with the characteristic?

P(x 470)= __?__ (Round to four decimal places as needed.)

(c) What is the probability of obtaining x= 420 or fewer individuals with the characteristic?

P(x <_ 470)= __?__ (Round to four decimal places as needed.)

Explanation / Answer

A) Describe the sampling distribution of p^.

given n=1000

p=0.44

standard deviation = sqrt(0.44*(1-0.44)/1000)= 0.01569

Answer: b) Approximately normal, mean = 0.44 and standard deviation approximately 0.0157

B) What is the probability of obtaining x=390 or more individuals with the characteristic? P(x>=390).

mean=n*p=1000*0.44 =440

standard devaiton =sqrt(1000*0.44*(1-0.44)) =15.697

So P(X>=470) = P((X-mean)/s >(470-440)/15.697)

=P(Z>1.91) = 1-0.9719 =0.0281(from standard normal table)

C) What is the probability of obtaining x=4700 or fewer individuals with the characteristic? P(x<=470).

P(X<=470) = P(Z<(470-440)/15.697)

=P(Z<1.91) =0.9719

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