Question

Suppose a simple random sample of size nequals150 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 0.8 . 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 greater than or equals 10. D. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 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 xequals126 or more individuals with the​ characteristic? That​ is, what is ​P(ModifyingAbove p with caretgreater than or equals0.84​)? ​P(ModifyingAbove p with caretgreater than or equals0.84​)equals nothing ​(Round to four decimal places as​ needed.) ​(c) What is the probability of obtaining xequals108 or fewer individuals with the​ characteristic? That​ is, what is ​P(ModifyingAbove p with caretless than or equals0.72​)? ​P(ModifyingAbove p with caretless than or equals0.72​)equals nothing ​(Round to four decimal places as​ needed.)

Answer 1