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According to a research institution, the average hotel price in a certain year was $105.12. Assume the population standard deviation is $20.00 and that a random sample of 32 hotels was selected. Complete parts a through d below. a. Calculate the standard error of the mean. (Round to two decimal places as needed.) b. What is the probability that the sample mean will be less than $106? P(x<$106) (Round to four decimal places as needed.) c. What is the probability that the sample mean will be more than $110? P(x> $110)- (Round to four decimal places as needed.) d. What is the probability that the sample mean will be between $103 and $105? P ($103 sxs$105) (Round to four decimal places as needed.)

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