Answer :
The likelihood that at least 150 people will collaborate and react in a fresh sample of 400 telephone numbers is 0.9953.
Describe probability?
The probability informs us of the likelihood that an event will occur. It is necessary for the likelihood to fall between 0 and 1. The likelihood of success is 1, whereas the probability of failure is 0.
Given, that the market research company has a history of having a 44% response rate for its telephone surveys.
Therefore, p=44%=0.44=μ
n=400
p=150/400
p=0.375
The standard deviation is then equal to,
σ=√(p(1-p))/n
σ=√(0.44(1-0.44))/400
σ=√(0.44×0.56)/400
σ=0.025
Using the z-table, the values are as follows:
z=(p-μ)/σ
z=(0.375-0.44)/0.025
z=-2.6
p(p>0.375)
=p(z>-2.6)
=1-p(z<-2.6)
=1-0.0047
=0.9953
=99.53%
Therefore, the likelihood that at least 150 people will participate and provide information in a new sample of 400 telephone numbers
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