Question 1

Z is a standard normal random variable. The P(-1.5 $\le$ z $\le$ 1.09) equals

Accepted Answer

A) 0.4322 
B) 0.3621 
C) 0.7953 
D) 0.0711

Question 2

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

Accepted Answer

A) cumulative probabilities for a standard normal z value 
B) the standard normal z value given a cumulative probability 
C) cumulative probabilities for a normally distributed x value 
D) the normally distributed x value given a cumulative probability

Question 3

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?

Accepted Answer

The answer of The monthly earnings of computer programmers are...

Question 4

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

Accepted Answer

A) The mean, median, and the mode are equal 
B) The mean of the distribution can be negative, zero, or positive 
C) The distribution is symmetrical 
D) The standard deviation must be 1

Question 5

Z is a standard normal random variable. The P(z $\ge$ 2.11) equals

Accepted Answer

A) 0.4821 
B) 0.9821 
C) 0.5 
D) 0.0174

Question 6

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-1. The probability that x will take on a value between 21 and 25 is

Accepted Answer

A) 0.125 
B) 0.250 
C) 0.500 
D) 1.000

Question 7

Z is a standard normal random variable. What is the value of z if the area between -z and z is 0.754?

Accepted Answer

A) 0.377 
B) 0.123 
C) 2.16 
D) 1.16

Question 8

The weights of items produced by a company are normally distributed with a mean of 4.5 ounces and a standard deviation of 0.3 ounces.
a.What is the probability that a randomly selected item from the production will weigh at least 4.14 ounces?
b.What percentage of the items weighs between 4.8 and 5.04 ounces?
c.Determine the minimum weight of the heaviest 5% of all items produced.
d.If 27,875 of the items of the entire production weigh at least 5.01 ounces, how many items have been produced?

Accepted Answer

The answer of The weights of items produced by a...

Question 9

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?

Accepted Answer

The answer of The weight of a .5 cubic yard...

Question 10

The standard deviation of a standard normal distribution

Accepted Answer

A) is always equal to zero 
B) is always equal to one 
C) can be any positive value 
D) can be any value

Question 11

Excel's NORM.S.INV function can be used to compute

Accepted Answer

A) cumulative probabilities for a standard normal z value 
B) the standard normal z value given a cumulative probability 
C) cumulative probabilities for a normally distributed x value 
D) the normally distributed x value given a cumulative probability

Question 12

The highest point of a normal curve occurs at

Accepted Answer

A) one standard deviation to the right of the mean 
B) two standard deviations to the right of the mean 
C) approximately three standard deviations to the right of the mean 
D) the mean

Question 13

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.

Accepted Answer

The answer of The Globe Fishery packs shrimp that weigh...

Question 14

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is

Accepted Answer

A) 0.1600 
B) 0.0160 
C) 0.0016 
D) 0.9452

Question 15

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
-Refer to Exhibit 6-1. The probability that x will take on a value of at least 26 is

Accepted Answer

A) 0.000 
B) 0.125 
C) 0.250 
D) 1.000

Question 16

Exhibit 6-7 
-The advertised weight on a can of soup is 10 ounces. The actual weight in the cans follows a uniform distribution and varies between 9.3 and 10.3 ounces.
a.Give the mathematical expression for the probability density function.
b.What is the probability that a can of soup will have between 9.4 and 10.3 ounces?
c.What is the mean weight of a can of soup?
d.What is the standard deviation of the weight?

Accepted Answer

The answer of Exhibit 6-7 
-The advertised weight on a...

Question 17

Z is a standard normal random variable. The P(1.05 $\le$ z $\le$ 2.13) equals

Accepted Answer

A) 0.8365 
B) 0.1303 
C) 0.4834 
D) None of the alternative answers is correct.

Question 18

Exhibit 6-6
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.
-Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of at least 47,500 miles?

Accepted Answer

A) 0.4332 
B) 0.9332 
C) 0.0668 
D) None of the alternative answers is correct.

Question 19

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 is the minimum weight of the middle 95% of the players?

Accepted Answer

A) 196 
B) 151 
C) 249 
D) None of the alternative answers is correct.

Question 20

Exhibit 6-6
The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles.
-Refer to Exhibit 6-6. What is the random variable in this experiment?

Accepted Answer

A) the life expectancy of this brand of tire 
B) the normal distribution 
C) 40,000 miles 
D) None of the alternative answers is correct.

Exam 6: Continuous Probability Distributions

Z is a standard normal random variable. The P(-1.5 ≤\le≤ z ≤\le≤ 1.09) equals

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

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?

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

Z is a standard normal random variable. The P(z ≥\ge≥ 2.11) equals

Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-1. The probability that x will take on a value between 21 and 25 is

Z is a standard normal random variable. What is the value of z if the area between -z and z is 0.754?

The standard deviation of a standard normal distribution

Excel's NORM.S.INV function can be used to compute

The highest point of a normal curve occurs at

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is

Exhibit 6-1 Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28. -Refer to Exhibit 6-1. The probability that x will take on a value of at least 26 is

Z is a standard normal random variable. The P(1.05 ≤\le≤ z ≤\le≤ 2.13) equals

Exhibit 6-6 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. -Refer to Exhibit 6-6. What is the probability that a randomly selected tire will have a life of at least 47,500 miles?

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 is the minimum weight of the middle 95% of the players?

Exhibit 6-6 The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 and a standard deviation of 5,000 miles. -Refer to Exhibit 6-6. What is the random variable in this experiment?

Z is a standard normal random variable. The P(-1.5 $\le$ z $\le$ 1.09) equals

Z is a standard normal random variable. The P(z $\ge$ 2.11) equals

Z is a standard normal random variable. The P(1.05 $\le$ z $\le$ 2.13) equals