Question

1. For each probability and percentile problem, draw the picture.

The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway varies from 14 to 35 mph and is uniformly distributed. None of the cars travel over 35 mph through the intersection.

Part (f)

σ =

Part (i) State "P(22 < X < 59) = ___" in a probability question.

Draw the picture and find the probability. (Enter your answer as a fraction.)

• Part (j)

  Find the 70th percentile.

  This means that 70% of the time, the speed is   mph while passing through the intersection.

• Part (k)

  Find the 75th percentile. In a complete sentence, state what this means.

This means that___% of the time, the speed is less than___mph while passing through the intersection.

Part (l) Find the probability that the speed is more than 27 mph given (or knowing that) it is at least 18 mph. (Enter your answer as a fraction.)

2. The average lifetime of a certain new cell phone is 4 years. The manufacturer will replace any cell phone failing within 2 years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution.

What is the decay rate? (Enter your answer as a fraction.)

Answer 1