Question

(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 greater than or equals 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 less than 10.np(1−p)<10.

C.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.Your answer is correct.

D.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.

Determine the mean of the sampling distribution of

ModifyingAbove p with caretp.

mu Subscript ModifyingAbove p with caret Baseline equalsμp=0.60.6

​(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=0.0692820.069282

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

​(b) What is the probability of obtaining

xequals=3232

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

​P(ModifyingAbove p with caretpgreater than or equals≥0.640.64​)?

​P(ModifyingAbove p with caretpgreater than or equals≥0.640.64​)equals=nothing

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

Answer 1

a) Approximately normal because n < 0.05N and np(1 - p) > 10.

= 0.6

= 0.069282

b) P( > 0.64)

= P(( - )/ > (0.64 - )/)

= P(Z > (0.64 - 0.6)/0.069282)

= P(Z > 0.58)

= 1 - P(Z < 0.58)

= 1 - 0.7190

= 0.2810