In 2021, CollegeData.com reported that books and materials cost an average of $1240 a year for students attending public

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In 2021, CollegeData.com reported that books and materials cost
an average of $1240 a year for students attending public or private
four-year colleges. Assume that the cost of books is normally
distributed with a standard deviation of $105.
a) What is the probability that a single student chosen at
random reports textbooks and materials costing more than $1362 for
an academic year?
b) Assuming the mean and standard deviation of textbook costs
have not changed, completely describe the sampling distribution for
the annual mean amount spent on books for a random sample of 15
students.
c) What is the probability that the annual mean cost of
textbooks and materials for a random sample of 15 students is
greater than $1362?
d) Considering your answer in part c, would you be willing to
conclude that the annual average cost of textbook prices is more
than $1240? Why or why not?