According to a researchinstitution, the average hotel price in a certain year was$97.27.Assume the population standard deviation is$21.00and that a random sample of 30hotels was selected. Complete parts a through d below.

a.Calculate the standard error of the mean.

=$

b.What is the probability that the sample mean will be less than $100?

P(x<$100)=

c. What is the probability that the sample mean will be more than $104?

P(x>$104)=