Question 1

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh more than 4.4 pounds is ?

Accepted Answer

0.0668

Question 2

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.What is the probability that a randomly selected can will containbetween 82 and 100 grams of tea leaves?

Accepted Answer

0.2132

Question 3

SCENARIO 6-4
According to Investment Digest, the arithmetic mean of the annual return for common stocks over an
85-year period was 9.5% but the value of the variance was not mentioned.Also 25% of the annual returns were below 8% while 65% of the annual returns were between 8% and 11.5%.The article claimed that the distribution of annual return for common stocks was bell-shaped and approximately symmetric.Assume that this distribution is normal with the mean given above.Answer the following questions without the help of a calculator, statistical software or statistical table.
-Referring to Scenario 6-4, 75% of the annual returns will be lower than what value?

Accepted Answer

11%

Question 4

SCENARIO 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 Scenario 6-3, what is the probability that a randomly selected orange will contain between 4.2 and 4.9 ounces of juices?

Accepted Answer

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

Question 5

If a data set is approximately normally distributed, its normal probability plot would be S-shaped.

Accepted Answer

A) True 
 B)False

Question 6

Theoretically, the mean, median, and the mode are all equal for a normal distribution.

Accepted Answer

A) True 
 B)False

Question 7

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.What is the probability that a randomly selected can will contain lessthan 100 grams of tea leaves?

Accepted Answer

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

Question 8

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh less than 2.2 pounds is ?

Accepted Answer

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

Question 9

The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes.The probability isthat a product is assembled in between 16 and 21 minutes.

Accepted Answer

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

Question 10

SCENARIO 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 $2000.At night he works occasionally 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 Scenario 6-2, for a given month, what is the probability that John's commission from the jewelry store is no more than $8,000?

Accepted Answer

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

Question 11

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z values are larger than is 0.3483.

Accepted Answer

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

Question 12

SCENARIO 6-5
Ball bearings are manufactured with a mean diameter of 6 millimeters (mm).Because of the inherent manufacturing process variability, the lots of bearings are approximately normally distributed with a standard deviation of 0.03 mm.
-Using Scenario 6-5, what proportion of ball bearings has a diameter of greater than 6 mm? NEW QUESTION

Accepted Answer

The answer of SCENARIO 6-5
Ball bearings are manufactured with a...

Question 13

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z values are larger than is 0.6985.

Accepted Answer

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

Question 14

If we know that the length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute, find the probability that a randomly selected college student will find a parking spot inthe library parking lot in less than 3 minutes.

Accepted Answer

A)  0.3551
B)  0.3085
C)  0.2674
D)  0.1915

Question 15

The value of the cumulative standardized normal distribution at Z is 0.8770.The value of Z is

Accepted Answer

A)  0.18
B)  0.81
C)  1.16
D)  1.47

Question 16

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is more than 0.77 is .

Accepted Answer

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

Question 17

SCENARIO 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 $2000.At night he works occasionally 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 Scenario 6-2, for a given month, what is the probability that John's income as a waiter is no more than $300?

Accepted Answer

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

Question 18

You were told that the amount of time elapsed between consecutive trades on a foreign stock exchange market followed a normal distribution with a mean of 15 seconds.You were also told that the probability that the time elapsed between two consecutive trades to fall between 16 to 17 seconds was 13%.The probability that the time elapsed between two consecutive trades would fall below 13 seconds was 7%.What is the probability that the time elapsed between two consecutive trades will be between 13 and 14 seconds?

Accepted Answer

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

Question 19

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is between -2.89 and -1.03 is _.

Accepted Answer

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

Question 20

The probability that a standard normal variable, Z, falls between -2.00 and -0.44 is 0.6472.

Accepted Answer

A) True 
 B)False

Exam 6: The Normal Distribution

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh more than 4.4 pounds is ?

The amount of tea leaves in a can from a production line is normally distributed with μ=110\mu = 110μ=110 grams and σ=25\sigma = 25σ=25 grams.What is the probability that a randomly selected can will containbetween 82 and 100 grams of tea leaves?

If a data set is approximately normally distributed, its normal probability plot would be S-shaped.

Theoretically, the mean, median, and the mode are all equal for a normal distribution.

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

The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound.Assuming the weights of catfish are normally distributed, the probability that a randomly selected catfish will weigh less than 2.2 pounds is ?

The amount of time necessary for assembly line workers to complete a product is a normal variable with a mean of 15 minutes and a standard deviation of 2 minutes.The probability isthat a product is assembled in between 16 and 21 minutes.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z values are larger than is 0.3483.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z values are larger than is 0.6985.

The value of the cumulative standardized normal distribution at Z is 0.8770.The value of Z is

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is more than 0.77 is .

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is between -2.89 and -1.03 is _.

The probability that a standard normal variable, Z, falls between -2.00 and -0.44 is 0.6472.

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.What is the probability that a randomly selected can will containbetween 82 and 100 grams of tea leaves?

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.What is the probability that a randomly selected can will contain lessthan 100 grams of tea leaves?