Question

Suppose a simple random sample of size nequals=7575 is obtained from a population whose size is Upper N equals 30 comma 000N=30,000 and whose population proportion with a specified characteristic is p equals 0.4 .p=0.4. Complete parts ​(a) through​ (c) below. ​(a) Describe the sampling distribution of ModifyingAbove p with caretp. Choose the phrase that best describes the shape of the sampling distribution below. A. Not normal because n less than or equals 0.05 Upper Nn≤0.05N and np left parenthesis 1 minus p right parenthesis less than 10.np(1−p)<10. B. Approximately normal because n less than or equals 0.05 Upper Nn≤0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1−p)≥10. C. Not normal because n less than or equals 0.05 Upper Nn≤0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1−p)≥10. D. Approximately normal because n less than or equals 0.05 Upper Nn≤0.05N and np left parenthesis 1 minus p right parenthesis less than 10.np(1−p)<10. Determine the mean of the sampling distribution of ModifyingAbove p with caretp. mu Subscript ModifyingAbove p with caret Baseline equalsμp=nothing ​(Round to one decimal place as​ needed.) Determine the standard deviation of the sampling distribution of ModifyingAbove p with caretp. sigma Subscript ModifyingAbove p with caretσpequals=nothing ​(Round to six decimal places as​ needed.) ​(b) What is the probability of obtaining xequals=3333 or more individuals with the​ characteristic? That​ is, what is ​P(ModifyingAbove p with caretpgreater than or equals≥0.440.44​)? ​P(ModifyingAbove p with caretpgreater than or equals≥0.440.44​)equals=nothing ​(Round to four decimal places as​ needed.) ​(c) What is the probability of obtaining xequals=2121 or fewer individuals with the​ characteristic? That​ is, what is ​P(ModifyingAbove p with caretpless than or equals≤0.280.28​)? ​P(ModifyingAbove p with caretpless than or equals≤0.280.28​)equals=nothing ​(Round to four decimal places as​ needed.)

Answer 1

(a)

Given that N = 30000, n=75 and p= 0.4

Now,

0.05*N = 0.05 * 30000 = 1500

That is n < = 0.05N

and np(1-p) = 75 * 0.4 * 0.6 = 18 >= 10

Correct option is:

B. Approximately normal because n less than or equals 0.05 Upper Nn≤0.05N and np left parenthesis 1 minus p right parenthesis greater than or equals 10.np(1−p)≥10.

(b)

(c)

(d)

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