Question

Collina’s Italian Café in Houston, Texas, advertises that carryout orders take about 25 minutes (Collina’s website, February 27, 2008). Assume that the time required for a carryout order to be ready for customer pickup has an exponential distribution with a mean of 25 minutes.

What is the probability than a carryout order will be ready within 20 minutes (to 4 decimals)?

Answer 1

You might try this formula:

Pr[T ≤ t] = 1 - e^-ht
h = reciprocal of the mean
t = time

Therefore, the reciprocal of 25 is 1/25 or .04

Substituting into the formula:
Pr[T ≤ 20] = 1 - e^-.04(20) = 1 - e^-.8 = 1 - .4493 = .5507

Check these calculations.

Answer 2

Jim Tree pays for shipping on the basis of weight. He knows weight is normally distributed so he can use the standard normal distribution. He decides to weigh 1,000 randomly trees in his shipment. Next, he calculates the mean and standard deviation of their weights. He finds the mean is 30 lbs and the standard deviation is 10 lbs. Now, Jim uses the normal distribution table to calculate the number of trees in each segment of the distribution.