Exam 6: The Normal Distributions and Other Continuous Distributions

SCENARIO 6-4 The interval between consecutive hits at a web site is assumed to follow an exponential distribution with a mean of 40 hits per minute. -Referring to Scenario 6-4, what is the mean time between consecutive hits?

The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes.So, 17% of the products would be assembled within __________ minutes.

A normal probability plot may be used to assess the assumption of normality for a set of data.

If a set of data is approximately normally distributed, we would find that approximately

A company that receives most of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of waiting time was found to be a variable best approximated by an exponential distribution with a mean length of waiting time equal to 2.8 minutes (i.e.the mean number of calls answered in a minute is 1/2.8).What is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?

SCENARIO 6-2 John has two jobs.For daytime work at a jewelry store he is paid $15,000 per month, plus a commission.His monthly commission is normally distributed with mean $10,000 and standard deviation $2000.At night he works occasionally as a waiter, for which his monthly income is normally distributed with mean $1,000 and standard deviation $300.John's income levels from these two sources are independent of each other. -Referring to Scenario 6-2, the probability is 0.45 that John's income as a waiter is more than how much in a given month?

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh more than 4.4 pounds is _______?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than 1.15 is __________.

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan.Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years.Find the age at which payments have ceased for approximately 86% of the plan participants.