Question 1

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than -0.98 is ________.

Accepted Answer

The answer of Suppose Z has a standard normal distribution...

Question 2

TABLE 6-3
A company producing orange juice buys all its oranges from a large orange orchard. The amount of juice that can be squeezed from each of these oranges is approximately normally distributed with a mean of 4.7 ounces and some unknown standard deviation. The company's production manager knows that the probability is 30.85% that a randomly selected orange will contain less than 4.5 ounces of juice. Also the probability is 10.56% that a randomly selected orange will contain more than 5.2 ounces of juice. Answer the following questions without the help of a calculator, statistical software, or statistical table.
-Referring to Table 6-3, what is the probability that a randomly selected orange will contain no more than 4.2 ounces of juice?

Accepted Answer

The answer of TABLE 6-3
A company producing orange juice buys...

Question 3

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is ________ that a product is assembled in between 14 and 16 minutes.

Accepted Answer

The answer of The amount of time necessary for assembly...

Question 4

TABLE 6-2
John has two jobs. For daytime work at a jewelry store he is paid $15,000 per month, plus a commission. His monthly commission is normally distributed with mean $10,000 and standard deviation $2,000. At night he works as a waiter, for which his monthly income is normally distributed with mean $1,000 and standard deviation $300. John's income levels from these two sources are independent of each other.
-Referring to Table 6-2, for a given month, what is the probability that John's income as a waiter is between $1,200 and $1,600?

Accepted Answer

The answer of TABLE 6-2
John has two jobs. For daytime...

Question 5

TABLE 6-1
The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean of 320 and population standard deviation of 20 inches.
-Referring to Table 6-1, for a randomly chosen Monday, what is the probability there will be less than 340 column inches of classified advertisement?

Accepted Answer

The answer of TABLE 6-1
The number of column inches of...

Question 6

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is ________ that a product is assembled in less than 20 minutes.

Accepted Answer

The answer of The amount of time necessary for assembly...

Question 7

TABLE 6-2
John has two jobs. For daytime work at a jewelry store he is paid $15,000 per month, plus a commission. His monthly commission is normally distributed with mean $10,000 and standard deviation $2,000. At night he works as a waiter, for which his monthly income is normally distributed with mean $1,000 and standard deviation $300. John's income levels from these two sources are independent of each other.
-Referring to Table 6-2, the probability is 0.25 that John's income as a waiter is no more than how much in a given month?

Accepted Answer

The answer of TABLE 6-2
John has two jobs. For daytime...

Question 8

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above what weight (in pounds)do 89.80% of the weights occur?

Accepted Answer

The answer of The owner of a fish market determined...

Question 9

The probability that a standard normal random variable, Z, is below 1.96 is 0.4750.

Accepted Answer

A) True 
 B)False

Question 10

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So 50% of the possible Z values are between ________ and ________ (symmetrically distributed about the mean).

Accepted Answer

The answer of Suppose Z has a standard normal distribution...

Question 11

A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is approximately a normal distribution with a mean of 68 years and a standard deviation of 3.5 years. Find the age at which payments have ceased for approximately 86% of the plan participants.

Accepted Answer

The answer of A company that sells annuities must base...

Question 12

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is ________ that a product is assembled in between 15 and 21 minutes.

Accepted Answer

The answer of The amount of time necessary for assembly...

Question 13

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain between 100 and 110 grams of tea leaves?

Accepted Answer

The answer of The amount of tea leaves in a...

Question 14

You were told that the amount of time lapsed between consecutive trades on the New York Stock Exchange followed a normal distribution with a mean of 15 seconds. You were also told that the probability that the time lapsed between two consecutive trades to fall between 16 to 17 seconds was 13%. The probability that the time lapsed between two consecutive trades would fall below 13 seconds was 7%. What is the probability that the time lapsed between two consecutive trades will be between 15 and 16 seconds?

Accepted Answer

The answer of You were told that the amount of...

Question 15

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain at least 100 grams of tea leaves?

Accepted Answer

The answer of The amount of tea leaves in a...

Question 16

TABLE 6-2
John has two jobs. For daytime work at a jewelry store he is paid $15,000 per month, plus a commission. His monthly commission is normally distributed with mean $10,000 and standard deviation $2,000. At night he works as a waiter, for which his monthly income is normally distributed with mean $1,000 and standard deviation $300. John's income levels from these two sources are independent of each other.
-Referring to Table 6-2, for a given month, what is the probability that John's income as a waiter is between $800 and $900?

Accepted Answer

The answer of TABLE 6-2
John has two jobs. For daytime...

Question 17

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. A citation catfish should be one of the top 2% in weight. Assuming the weights of catfish are normally distributed, at what weight (in pounds)should the citation designation be established?

Accepted Answer

A)  1.56 pounds 
B)  4.84 pounds 
C)  5.20 pounds 
D)  7.36 pounds

Question 18

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So 85% of the possible Z values are smaller than ________.

Accepted Answer

The answer of Suppose Z has a standard normal distribution...

Question 19

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 17% of the products would be assembled within ________ minutes.

Accepted Answer

The answer of The amount of time necessary for assembly...

Question 20

The probability that a standard normal random variable, Z, falls between -1.50 and 0.81 is 0.7242.

Accepted Answer

A) True 
 B)False

Exam 6: The Normal Distribution

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is more than -0.98 is ________.

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is ________ that a product is assembled in between 14 and 16 minutes.

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is ________ that a product is assembled in less than 20 minutes.

The owner of a fish market determined that the average weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. Assuming the weights of catfish are normally distributed, above what weight (in pounds)do 89.80% of the weights occur?

The probability that a standard normal random variable, Z, is below 1.96 is 0.4750.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So 50% of the possible Z values are between and (symmetrically distributed about the mean).

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. The probability is ________ that a product is assembled in between 15 and 21 minutes.

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain between 100 and 110 grams of tea leaves?

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected can will contain at least 100 grams of tea leaves?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. So 85% of the possible Z values are smaller than ________.

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes. So, 17% of the products would be assembled within ________ minutes.

The probability that a standard normal random variable, Z, falls between -1.50 and 0.81 is 0.7242.