Exam 7: Continuous Probability Distributions

The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches. What proportion of brook trout caught will be between 12 and 18 inches in length?

In Melanie's Styling Salon, the time to complete a simple haircut is normally distributed with a mean of 25 minutes and a standard deviation of 4 minutes. The slowest quartile of customers will require longer than how many minutes for a simple haircut?

The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches. The first quartile for the lengths of brook trout would be:

A random variable X is best described by a continuous uniform distribution from 20 to 45 inclusive. What is P(30 ≤ X ≤ 40)?

A machine dispenses water into a glass. Assuming that the amount of water dispensed follows a continuous uniform distribution from 10 ounces to 16 ounces, what is the probability that 13 or more ounces will be dispensed in a given glass?

The triangular distribution is used in "what-if" analysis for business planning.

The figure shows a normal N(400, 23) distribution. Find the approximate shaded area. C.2 gives 1 - P(z < 0.74) = 1 - .7704 = .2296, or from Excel =1-NORM.DIST(417,400,23,1) = .2299.

The triangular distribution is symmetric.

If arrivals follow a Poisson distribution, waiting times follow the exponential distribution.

Exam scores were normal in BIO 200. Jason's exam score was one standard deviation above the mean. What percentile is he in?

What are the mean and standard deviation for the standard normal distribution?

In Melanie's Styling Salon, the time to complete a simple haircut is normally distributed with a mean of 25 minutes and a standard deviation of 4 minutes. For a simple haircut, the middle 90 percent of the customers will require:

The figure shows a standard normal N(0, 1) distribution. Find the shaded area. C.2. gives 1 - P(z < .44) = 1 - .6700 = .3300 =1-NORM.S.DIST(0.44,1).

The exponential distribution is always skewed right.

The lengths of brook trout caught in a certain Colorado stream are normally distributed with a mean of 14 inches and a standard deviation of 3 inches. What lower limit should the State Game Commission set on length if it is desired that 80 percent of the catch may be kept by fishers?

If arrivals occur at a mean rate of 2.6 events per minute, the exponential probability of waiting more than 1.5 minutes for the next arrival is:

In a continuous distribution:

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. The slowest 10 percent of the citizens would need at least how many minutes to complete the form?

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 proportion of the citizens will require less than one hour?

If the mean waiting time for the next arrival is 18 minutes, what is the first quartile (25^th percentile) for waiting times?