Question 1

You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 60 and 95?

Accepted Answer

The answer of You were told that the mean score...

Question 2

TABLE 6-7
A company has 125 personal computers. The probability that any one of them will require repair on a given day is 0.15.
-Referring to Table 6-7 and assuming that the number of computers that requires repair on a given day follows a binomial distribution, compute the probability that there will be exactly 10 computers that require repair on a given day using a normal approximation.

Accepted Answer

The answer of TABLE 6-7
A company has 125 personal computers....

Question 3

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be more than 5 minutes?

Accepted Answer

The answer of Patients arriving at an outpatient clinic follow...

Question 4

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. What proportion of the plan recipients die before they reach the standard retirement age of 65?

Accepted Answer

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

Question 5

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of
The probability that Z is less than -2.20 is____ .

Accepted Answer

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

Question 6

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, the probability that a randomly selected catfish will weigh between 3 and 5 pounds is_____ .

Accepted Answer

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

Question 7

TABLE 6-4
John has two jobs. For daytime work at a jewelry store he is paid $200 per month, plus a commission. His monthly commission is normally distributed with mean $600 and standard deviation $40. At night he works as a waiter, for which his monthly income is normally distributed with mean $100 and standard deviation $30. John's income levels from these two sources are independent of each other.
-Referring to Table 6-4, for a given month, what is the probability that John's total income from these two jobs is less than $825?

Accepted Answer

The answer of TABLE 6-4
John has two jobs. For daytime...

Question 8

TABLE 6-2
The city manager of a large city believes that the number of reported accidents on any weekend has a normal distribution. She takes a sample of nine weekends and determines the number of reported accidents during each. The ordered array for this data is: 15, 46, 53, 54, 55, 76, 82, 256, 407.
-Referring to Table 6-2, the first standard normal quantile is ______ .

Accepted Answer

The answer of TABLE 6-2
The city manager of a large...

Question 9

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be between 5 minutes and 15 minutes?

Accepted Answer

The answer of Patients arriving at an outpatient clinic follow...

Question 10

You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score lower than 55?

Accepted Answer

The answer of You were told that the mean score...

Question 11

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 12

TABLE 6-2
The city manager of a large city believes that the number of reported accidents on any weekend has a normal distribution. She takes a sample of nine weekends and determines the number of reported accidents during each. The ordered array for this data is: 15, 46, 53, 54, 55, 76, 82, 256, 407.
-Referring to Table 6-2, the fifth standard normal quantile is_____ .

Accepted Answer

The answer of TABLE 6-2
The city manager of a large...

Question 13

The probability that a standard normal variable Z is positive is_____ .

Accepted Answer

The answer of The probability that a standard normal variable...

Question 14

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. What proportion of the plan recipients would receive payments beyond age 75?

Accepted Answer

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

Question 15

You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. The middle 95.46% of the students will score between which two scores?

Accepted Answer

The answer of You were told that the mean score...

Question 16

TABLE 6-2
The city manager of a large city believes that the number of reported accidents on any weekend has a normal distribution. She takes a sample of nine weekends and determines the number of reported accidents during each. The ordered array for this data is: 15, 46, 53, 54, 55, 76, 82, 256, 407.
-Referring to Table 6-2, the seventh standard normal quantile is _____ .

Accepted Answer

The answer of TABLE 6-2
The city manager of a large...

Question 17

TABLE 6-5
Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes.
-Referring to Table 6-5, what is the probability that the time interval between two consecutive defective light bulbs will be between 10 and 35 minutes?

Accepted Answer

The answer of TABLE 6-5
Suppose the time interval between two...

Question 18

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of
The probability that Z is less than 1.15 is______ .

Accepted Answer

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

Question 19

TABLE 6-3
The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean 320 and population standard deviation 20 inches.
-Referring to Table 6-3, 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 6-3
The number of column inches of...

Question 20

TABLE 6-4
John has two jobs. For daytime work at a jewelry store he is paid $200 per month, plus a commission. His monthly commission is normally distributed with mean $600 and standard deviation $40. At night he works as a waiter, for which his monthly income is normally distributed with mean $100 and standard deviation $30. John's income levels from these two sources are independent of each other.
-Referring to Table 6-4, for a given month, what is the probability that John's commission from the jewelry store is less than $640?

Accepted Answer

The answer of TABLE 6-4
John has two jobs. For daytime...

Quiz 6: The Normal Distribution and Other Continuous Distributions

You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 60 and 95?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be more than 5 minutes?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of The probability that Z is less than -2.20 is____ .

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, the probability that a randomly selected catfish will weigh between 3 and 5 pounds is_____ .

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 15 patients per hour. What is the probability that a randomly chosen arrival to be between 5 minutes and 15 minutes?

You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score lower than 55?

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 probability that a standard normal variable Z is positive is_____ .

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of The probability that Z is less than 1.15 is______ .