Question

A market research firm conducts telephone surveys with a 41% historical response rate. a. What is the probability that in a new sample of 400 telephone numbers, at least 135 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 135/400 = 0.3375?

Answer 1

probability is 0.778

Explanation:

Given data in question

success of probability (p) = 41% = 0.41

no of sample (n) = 400

individual = 150

to find out

probability that the sample proportion will be at least 135/400

solution

first we calculate the mean i.e

mean = p × n

mean = 400 × 0.41

mean = 164

now we calculate standard deviation =
`√(400(0.41) 0.59)`

standard deviation = 9.83666

we know P(X ≥ 135) = P(Z ≥ (150 - 164)/9.83666)

P(X ≥ 135) = P(Z ≥ (-1.42324)

from table 1 find corresponding probability

P(X ≥ 135) = 1 - P(Z ≥ (-1.42324)

= 1 - 0.9222 = 0.778

probability is 0.778