Exam 7: Continuous Probability Distributions

Excel's =100*RAND() function produces continuous random numbers that are uniformly distributed between 0 and 100. The standard deviation of this distribution is approximately:

If the random variable Z has a standard normal distribution, then P(1.25 ≤ Z ≤ 2.17) is:

If the random variable Z has a standard normal distribution, then P(Z ≤ -1.37) is:

A continuous uniform distribution is always symmetric.

For a continuous uniform distribution U(200, 400), the parameters are μ = 300 and σ = 100.

Which statement is incorrect?

We would use a normal distribution to model the waiting time until the next Florida hurricane strike.

Historically, the default rate on a certain type of commercial loan is 20 percent. If a bank makes 100 of these loans, what is the approximate probability that at least 26 will result in default?

The figure shows a standard normal N(0, 1) distribution. Find the z value for the shaded area. C.2 gives P(z < -1.75) = .0401 or use Excel =NORM.S.INV(0.04) = -1.75.

Any normal distribution has a mean of 0 and a standard deviation of 1.

Compared to the area between z = 0.50 and z = 0.75, the area between z = 1.50 and z = 1.75 in the standard normal distribution will be:

The time required for a citizen to complete the 2010 U.S. Census "long" form is normally distributed with a mean of 40 minutes and a standard deviation of 10 minutes. What is the third quartile (in minutes) for the time required to complete the form?

The probability that a rental car will be stolen is 0.001. If 25,000 cars are rented from Hertz, what is the normal approximation to the probability that fewer than 20 will be stolen?

TotCo is developing a new deluxe baby bassinet. If the length of a newborn baby is normally distributed with a mean of 50 cm and a standard deviation of 5 cm, what should be the interior length of the bassinet to ensure that 99 percent of newborn babies will fit, with a safety margin of 15 cm on each end of the bassinet?

A certain assembly line at Vexing Manufacturing Company averages 30 minutes between breakdowns. What is the probability that less than 6 minutes will elapse before the next breakdown?

Any two normal curves are the same except for their:

A letter is mailed to a sample of 500 homeowners. Based on past experience, the probability of an undeliverable letter is 0.06. The normal approximation to the binomial probability of 40 or more undeliverable letters is:

A triangular distribution can be skewed either left or right.

There is a simple formula for normal areas, but we prefer a table for greater accuracy.

For which binomial distribution would a normal approximation be most acceptable?