1. The number of gallons of ice cream ordered at JJ Ice Cream on a hot summer day has the following probability density

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1. The number of gallons of ice cream ordered at JJ Ice Cream ona hot summer day has the following probability densityfunctionf(x)=
for
0 ≤ x ≤ 100
and 0 otherwise.a) What is the probability that X > 50? b) What is the probability that X < 50? c) What is the probability that 25 < X < 75? d) What is the expected value of X (E(X))? e) What is the expected value of X - 5? f) What is the expected value of 6X? g) What is the expected value of
X2
? h) What is the probability that X is less than its expectedvalue? i) What is the expected value of
X2+3X+1
? j) What is the 70th percentile of X? k) What is the probability that X is within 30 of its expectedvalue? l) What is the probability that X = 71?