According to an industry report, 26 percent of all households have at least one
ID: 3433705 • Letter: A
Question
According to an industry report, 26 percent of all households have at least one cell phone. Further, of those that do have a cell phone, the mean monthly bill is $55.90 with a standard deviation equal to $9.60. Recently, a random sample of 400 households was selected. Of these households, 88 indicated that they had cell phones. The mean bill for these 88 households was $57.00. What is the probability of getting 88 or fewer households with cell phones if the numbers provided by the industry report are correct?
Explanation / Answer
Solution :
If N=400 and p=.26
Pr[N<=88]=.0369
I used a powerful statistical tool that calculates cumulative Binomial Probabilities
You can use Excel or some other online Binomial calculator
if you wanted to use a Normal Approximation
mean=400(.26)=104
Var=104(1-.26)=76.96
Pr[Z<88.5-104/sqrt(76.96)]
=Pr[Z<-1.76685]=.0386, not a bad approximation considering the exact probability
is .0369. In fact, to two decimal places, the Normal Approximation and The exact
Binomial probability both yield .04.
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