Exam 6: Continuous Probability Distributions

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. The probability of a player weighing more than 241.25 pounds is

"DRUGS R US" is a large manufacturer of various kinds of liquid vitamins. The quality control department has noted that the bottles of vitamins marked 6 ounces vary in content with a standard deviation of 0.3 ounces. Assume the contents of the bottles are normally distributed. a.What percentage of all bottles produced contains more than 6.51 ounces of vitamins? b.What percentage of all bottles produced contains less than 5.415 ounces? c.What percentage of bottles produced contains between 5.46 and 6.495 ounces? d.Ninety-five percent of the bottles will contain at least how many ounces? e.What percentage of the bottles contains between 6.3 and 6.6 ounces?

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.1112?

The exponential probability distribution is used with

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 percentage of items will weigh at least 11.7 ounces?

In grading eggs into small, medium, and large, the Linda Farms packs the eggs that weigh more than 3.6 ounces in packages marked "large" and the eggs that weigh less than 2.4 ounces into packages marked "small"; the remainder are packed in packages marked "medium." If a day's packaging contained 10.2% large and 4.18% small eggs, determine the mean and the standard deviation for the eggs' weights. Assume that the distribution of the weights is normal.

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The standard deviation of assembly time (in minutes) is approximately

Exhibit 6-7 -The length of time it takes students to complete a statistics examination is uniformly distributed and varies between 40 and 60 minutes. a.Find the mathematical expression for the probability density function. b.Compute the probability that a student will take between 45 and 50 minutes to complete the examination. c.Compute the probability that a student will take no more than 40 minutes to complete the examination. d.What is the expected amount of time it takes a student to complete the examination? e.What is the variance for the amount of time it takes a student to complete the examination?

The 9-month salaries at a daycare center are normally distributed with a mean of $19,000 and a standard deviation of $4,000. a.What is the probability that an employee will have a salary between $12,520 and $13,480? b.What is the probability that an employee will have a salary more than $11,880? c.What is the probability that an employee will have a salary less than $28,440?

Exhibit 6-7 -The skewness measure for the exponential distributions is

The township of Middleton sets the speed limit on its roads by conducting a traffic study and determining the speed (to the nearest 5 miles per hour) at which 80% of the drivers travel at or below. A study was done on Brown's Dock Road that indicated driver's speeds follow a normal distribution with a mean of 36.25 miles per hour and a variance of 6.25. a. What should the speed limit be? b. What percent of the drivers travel below that speed?

When using Excel's EXPON.DIST function, one should choose TRUE for the third input if

The form of the continuous uniform probability distribution is

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 is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

The probability density function for a uniform distribution ranging between 2 and 6 is

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?

Exhibit 6-7 -The price of a bond is uniformly distributed between $80 and $85. a.What is the probability that the bond price will be at least $83? b.What is the probability that the bond price will be between $81 and $90? c.Determine the expected price of the bond. d.Compute the standard deviation for the bond price.

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 is the random variable in this experiment?

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

For a continuous random variable x, the probability density function f(x) represents