Question

A market research firm conducts telephone surveys with a 42% historical response rate. What is the probability that in a new sample of 375 telephone numbers, at least 150 individuals will cooperate and respond to the questions

Answer 1

The right answer is "0.7823".

Explanation:

Given that,

P = 42%

or,

= 0.42

n = 375

`\hat{P}` = 0.4

The z-score will be:

=
`\frac{\hat{P}-\mu_P}{\sigma_p}`

By putting the values, we get

=
`\frac{0.4-0.42}{\sqrt{(0.42* (1-0.42))/(0.375) } }`

=
`-0.784706`

hence,

The probability will be:

⇒
`P(\hat {P}>0.04)` =
`P(z>-0.7847)`

=
`1-P(z<-0.7847)`

=
`1-0.21770`

=
`0.7823`