Question

Suppose a simple random sample of size nequals=1000is obtained from a population whose size is Nequals=1,500,000 and whose population proportion with a specified characteristic is p equals 0.44 .p=0.44. Complete parts (a) through (c) below. (a) Describe the sampling distribution of ModifyingAbove p with cartel.(b) What is the probability of obtaining xequals=480or more individuals with the characteristic? P(xgreater than or equals≥480480 )equals=nothing (Round to four decimal places as needed.) (c) What is the probability of obtaining xequals=420 or fewer individuals with the characteristic? P(xless than or equals≤420420 )equals=nothing (Round to four decimal places as needed.)

Answer 1

solution:-

given that n = 1000 , p = 0.44

(a) Describe the sampling distribution of p^

μp = 0.44 and σp = sqrt(p*(1-p)/n) = sqrt(0.44*(1-0.44)/1000) = 0.0157

=> Approximately normal μp = 0.44 and σp = 0.0157

(b) P(x ≥ 480) then p^ = 480/1000 = 0.48

=> P(z ≥ (0.48-0.44)/0.0157)

=> P(z > 2.55)

=> 1 - P(z < 2.55)

=> 1 - 0.9946

=> 0.0054

(c) P(x ≤ 420) then p^ = 420/1000 = 0.42

=> P(z ≤ (0.42-0.44)/0.0157)

=> P(z ≤ -1.27)

=> 1 - P(z < 1.27)

=> 1 - 0.8980

=> 0.1020