Maria is shopping for wireless routers and is overwhelmed by the number of optio
ID: 3125245 • Letter: M
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 73 dollars and the standard deviation is 18 dollars.
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 18 dollars(i.e., if we assume Marias 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 73 dollars? Give your answer to three decimal places.
Explanation / Answer
Given average price of all routers = $80; standard deviation = $18
sample size n =75
standard deviation of sample mean = 18/sqrt(75) = 2.0785
Let X be average price of 73 routers
P( X<=73) = P[z<= (73-80)/2.0785) = P(z<=-3.36788) = 0.0004=0.000