Question

Suppose a simple random sample of size nequals50 is obtained from a population whose size is Upper N equals 15 comma 000 and whose population proportion with a specified characteristic is p equals 0.6 . Complete parts ​(a) through​ (c) below. ​(a) Describe the sampling distribution of ModifyingAbove p with caret. Choose the phrase that best describes the shape of the sampling distribution below. A. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10. B. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10. C. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10. D. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10. Determine the mean of the sampling distribution of ModifyingAbove p with caret. mu Subscript ModifyingAbove p with caret Baseline equals nothing ​(Round to one decimal place as​ needed.) Determine the standard deviation of the sampling distribution of ModifyingAbove p with caret. sigma Subscript ModifyingAbove p with caretequals nothing ​(Round to six decimal places as​ needed.) ​(b) What is the probability of obtaining xequals31 or more individuals with the​ characteristic? That​ is, what is ​P(ModifyingAbove p with caretgreater than or equals0.62​)? ​P(ModifyingAbove p with caretgreater than or equals0.62​)equals nothing ​(Round to four decimal places as​ needed.)

c) What is the probability of obtaining

xequals=2727

or fewer individuals with the​ characteristic? That​ is, what is

​P(ModifyingAbove p with caretpless than or equals≤0.540.54​)?

​P(ModifyingAbove p with caretpless than or equals≤0.540.54​)equals=nothing

​(Round to four decimal places as​ needed.)

Answer 1

The sample size is and the population size is . Here .

We see . Also

Both greater than 10.

a) The sampling distribution of is normal since,

D. Approximately normal because and

The standard deviation of the sampling distribution of is

b) The probability,

c) The probability,

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