Exam 6: Continuous Probability Distributions

The Globe Fishery packs shrimp that weigh more than 1.91 ounces each in packages marked" large" and shrimp that weigh less than 0.47 ounces each into packages marked "small"; the remainder are packed in "medium" size packages. If a day's catch showed that 19.77% of the shrimp were large and 6.06% were small, determine the mean and the standard deviation for the shrimp weights. Assume that the shrimps' weights are normally distributed.

Z is a standard normal random variable. The P(1.20  z  1.85) equals

X is a exponentially distributed random variable with a mean of 10. Use Excel to calculate the following: a.P(x  15) b.P(8  x  12) c.P(x  8)

X is a normally distributed random variable with a mean of 50 and a standard deviation of 5. Use Excel to calculate the following: a.P(x  45) b.P(45  x  55) c.P(x  55) d.x value with .20 in the lower tail e.x value with .01 in the upper tail

Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. -Refer to Exhibit 6-3. What percent of players weigh between 180 and 220 pounds?

The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 8 minutes. a.What is the probability density function for the time it takes to complete the task? b.What is the probability that it will take a worker less than 4 minutes to complete the task? c.What is the probability that it will take a worker between 6 and 10 minutes to complete the task?

The miles-per-gallon obtained by the 2010 model Q cars is normally distributed with a mean of 22 miles-per-gallon and a standard deviation of 5 miles-per-gallon. a.What is the probability that a car will get between 13.35 and 35.1 miles-per-gallon? b.What is the probability that a car will get more than 29.6 miles-per-gallon? c.What is the probability that a car will get less than 21 miles-per-gallon? d.What is the probability that a car will get exactly 22 miles-per-gallon?

Which of the following is not a characteristic of the normal probability distribution?

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The probability of assembling the product in 7 minutes or more is

Exhibit 6-7 -Refer to Exhibit 6-7. The probability that x is less than 5 is

Excel's EXPON.DIST function has how many inputs?

Exhibit 6-4 The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. -Refer to Exhibit 6-4. What percentage of MBA's will have starting salaries of $34,000 to $46,000?

Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces. -Refer to Exhibit 6-5. What is the probability that a randomly selected item weighs exactly 8 ounces?

The weight of a .5 cubic yard bag of landscape mulch is uniformly distributed over the interval from 38.5 to 41.5 pounds. a. Give a mathematical expression for the probability density function. b. What is the probability that a bag will weigh more than 40 pounds? c. What is the probability that a bag will weigh less than 39 pounds? d. What is the probability that a bag will weigh between 39 and 40 pounds?

The monthly earnings of computer programmers are normally distributed with a mean of $4,000. If only 1.7 percent of programmers have monthly incomes of less than $2,834, what is the value of the standard deviation of the monthly earnings of the computer programmers?

Z is a standard normal random variable. Compute the following probabilities. a.P(-1.33  z  1.67) b.P(1.23  z  1.55) c.P(z  2.32) d.P(z  -2.08) e.P(z  -1.08)

Excel's EXPON.DIST function can be used to compute

The form of the continuous uniform probability distribution is

If the mean of a normal distribution is negative,

The average starting salary of this year's vocational school graduates is $35,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. What are the minimum and the maximum starting salaries of the middle 95% of the graduates?