Question

A market research firm conducts telephone surveys with a 47% historical response rate. If 75 individuals are contacted, find the probability that 36 or less of them will cooperate and respond to the survey questions.

Answer 1

Here we have given that

Market research firm conducts telephone surveys with a 47% historical response rate.

P= population proportion=47%=0.47

n= Number of individuals contacted = 75

Now, we want to find the probability that 36 or less of them will operate and respond to the survey questions.

x: Number of individuals respond to the survey questions=36

= sample proportion =

Here, to find the probability, we want to use the normal approximation to the binomial

n*P= 75*0.47 =35 > 10

n*(1-P)= 75*(1-0.47) =40  >10

Here, we can use the normal approximation to the normal

We know that

the mean of all sample proportion is the population proportion.

= P = 0.47

And

=  

=

=0.058

Now, we want to find the probability that 36 or less of them will operate and respond to the survey questions.

i.e

= converting to the standard normal z

=

=

=0.5675

The probability that 36 or less of them will operate and respond to the survey questions is 0.5675

i.e =0.5675