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?
A) Approximately 0.0344
B) Nearly 0.4656
C) About 0.1345
D) Can't be determined without knowing the standard deviation

Question

Quizplus · Accepted Answer

The probability of getting 88 or fewer households with cell phones can be calculated using the binomial distribution or normal approximation to the binomial distribution. Given that 26% of all households have at least one cell phone, for a sample of 400 households, the expected number of households with a cell phone is 0.26 * 400 = 104. The question asks for the probability of getting 88 or fewer households, which can be calculated using the normal approximation because the sample size is large. The calculation involves finding the z-score and then the corresponding probability. The answer does not depend on the mean monthly bill or its standard deviation, as those relate to a different part of the scenario.

According to an Industry Report, 26 Percent of All Households