1. The average daily temperature in Dublin during the month of May (n = 31 days)

is assumed to be a random variable with mean 15 (Celsius degrees) and standard

deviation o = 4. Assume that the daily values are independent of one another.

(a) Use Chebyshev's inequality to upper bound the probability that the average

temperature of a given day exceeds 25 degrees.

(b) Use Chebyshev's inequality to upper bound the probability that the monthly

average (obtained from the average daily temperatures) is greater than 16.5

degrees.

(c) Use the central limit theorem to approximate the probability that the monthly

average (obtained from the average daily temperatures) is greater than 16.5

degrees.