The number of minutes of hot water you can expect from the shower in your dormit

ID: 3066267 • Letter: T

Question

The number of minutes of hot water you can expect from the shower in your dormitory is defined by the continuous probability density function:

f(x)= {1/5 for x values between 1 and 6 minutes; 0 everywhere else }

Where x = values for the random variable “minutes of hot water.”

Determine the probability that you will have between 5 and 5.5 minutes of hot water.

Determine the probability that you will have no more than 4.5 minutes of hot water.

Determine the mean (expected value) and the standard deviation of the “minutes of hot water” random variable.

Show that the total area associated with the probability density function is 1.0. That is demonstrate that P(1<= x <=6) =1.0

X ~ U(1 , 6) 1 < X < 6

a) P(5 < X < 5.5) = (5.5 - 5) / (6 - 1) = 0.1

b) P(X < 4.5) = (4.5 - 1) / (6 - 1) = 0.7

c) Mean = (1 + 6) / 2 = 3.5

Standard deviation = (6 - 1) / sqrt(12) = 1.44

d) Total area = (6 - 1) * (1/5) = 1

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