Question

Suppose a simple random sample of size n equals1000 is obtained from a population whose size is N equals1 comma 000 comma 000 and whose population proportion with a specified characteristic is p equals 0.31 . Complete parts​ (a) through​ (c) below.

​(a) Describe the sampling distribution of Modifying Above p with caret.

A. Approximately​ normal, mu Subscript Modifying Above p with caret equals 0.31 and sigma Subscript Modifying Above p with caret almost equals 0.0005

B. Approximately​ normal, mu Subscript Modifying Above p with caret equals 0.31 and sigma Subscript Modifying Above p with caret almost equals 0.0146

C. Approximately​ normal, mu Subscript Modifying Above p with caret equals 0.31 and sigma Subscript Modifying Above p with caret almost equals 0.0002

​(b) What is the probability of obtaining x equals 340 or more individuals with the​ characteristic? ​P(x greater than or equals 340​) equals nothing ​(Round to four decimal places as​ needed.)

​(c) What is the probability of obtaining x equals 290 or fewer individuals with the​ characteristic? ​P (x less than or equals 290​) equals nothing ​(Round to four decimal places as​ needed.)

Answer 1

(a)

n = 1000

N = 1,000,000

p = 0.31

Standard error of proportion, =

=

= 0.0146

Thus, the answer is,

B. Approximately​ normal, mu Subscript Modifying Above p with caret equals 0.31 and sigma Subscript Modifying Above p with caret almost equals 0.0146

(b)

P(x 340) = P(p 0.34)

= P(z (0.34 - 0.31)/0.0146)

= P(z 2.05)

= 0.0202

(c)

P(x 290) = P(p 0.29)

= P(z (0.29 - 0.31)/0.0146)

= P(z -1.37)

= 0.0853