Question

A recent report found that a local creamery has a 35% market share in a certain region. Employees in the marketing department of the creamery conduct a survey to confirm the results by randomly selecting 300 residents from the region. The employees asked the question "Which brand of ice cream do you usually purchase?" to each resident. Use a normal approximation to calculate the probability that at most 80 of these people will choose the creamery's brand. Use a TI-83, TI-83 plus, or TI-84 calculator to find the probability.

Answer 1

The local creamery has a 35% market share in a certain region. this means that the probability that a randomly selected resident from this region chooses the creamery's brand is 0.35

Let X be the number of residents out of 300 surveyed, who choose the creamery's brand. X has a Binomial distribution with parameters, number of trials (number of residents surveyed) n=300 and success probability (the probability that a randomly selected resident from this region chooses the creamery's brand) p=0.35.

The mean (expected value) of X is

The standard deviation is

the probability that at most 80 (80 or less) of these people will choose the creamery's brand is

To calculate the above using TI-83, follow these steps

• Press 2nd+VARS, under DISTR and select normalcdf

The function takes normalcdf(lower bound,upper bound,mean, standard deviation). Here use the lower bound as -9999, upper bound is 80.5, mean=105 and standard deviation = 8.2614

Ans: the probability that at most 80 of these people will choose the creamery's brand is 0.0015