Maria is shopping for wireless routers and is overwhelmed by the number of optio

Question

Maria is shopping for wireless routers and is overwhelmed by the number of options. In order to get a feel for the average price, she takes a random sample of 75 routers. The average price for this sample is 74 and the standard deviation is 24. A consumer information website claims that the average price of all routers is $80. If we assume that the population standard deviation of prices is 24 (i.e., if we assume Maria's sample standard deviation is a good estimate of ), what is the probability that a random sample of 75 routers would have an average price of less than or equal to 7 You may assume that the sample mean follows a Normal distribution. Give your answer to three decimal places thet the sample mean folows a Norm , what is the probablity that t assume that the population Probability (Thus Maria's sample suggests strongly that the consumer information website is incorrect!)

Explanation / Answer

We have the normal distribution params here, and the we can normalize X to Z by using these params:

n = 75

Pop.Mean = 74

Stdev = 24

Sample.mean = 80

We normalize, as below:

P(X<=74) = P(Z<= (80-74)/(24/sqrt(75)) = P(Z<=2.16) = .985

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