5 The total amount of tips a waitress receives is uniformly

5. The total amount of tips a waitress receives is uniformly distributed between $1 and $25 in an hour on average.

(a) Find the probability the waitress receives between $15 and $20.

(b) What is the expected tip amount the waitress will receive?

(c) Find the following probabilities: P r(X < mX),P r(X > mX) where X =the amount of tips a waitress receives.

(d) What is the median amount of tips a waitress will receive?

Solution

a = $1
b = $25

a.
P(15<X<20)
= (20-15) / (25-1)
= 0.2083

b.
expected tip amount = (1+25)/2
= 13

c.
P(X<mean) = P(X>mean) = 0.50

d.
median = mean in uniform distribution
median = 13