Question 1

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 2

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 exactly 10 minutes?

Accepted Answer

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

Question 3

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes. What is the probability that a randomly chosen arrival to be more than 18 minutes?

Accepted Answer

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

Question 4

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 16 and 21 minutes.

Accepted Answer

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

Question 5

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 longer than 17 seconds?

Accepted Answer

The answer of You were told that the amount 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. So, 70% of the products would be assembled within ______ minutes.

Accepted Answer

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

Question 7

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour. What is the probability that a randomly chosen arrival to be more than
2.5 hours?

Accepted Answer

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

Question 8

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes. What is the probability that a randomly chosen arrival to be less than 15 minutes?

Accepted Answer

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

Question 9

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%. The middle 86% of the time lapsed will fall between which two numbers?

Accepted Answer

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

Question 10

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour. What is the probability that a randomly chosen arrival to be more than 1 hour?

Accepted Answer

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

Question 11

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 90 and 95?

Accepted Answer

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

Question 12

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%. The middle 60% of the time lapsed will fall between which two numbers?

Accepted Answer

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

Question 13

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 no more than 8 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 14

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

Accepted Answer

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

Question 15

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 standard deviation of the time interval?

Accepted Answer

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

Question 16

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of
 So 96% 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 17

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be between 121 and 124 inches?

Accepted Answer

The answer of The true length of boards cut at...

Question 18

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%. The probability is 80% that the time lapsed will be longer than how many seconds?

Accepted Answer

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

Question 19

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 income as a waiter is between $70 and $160?

Accepted Answer

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

Question 20

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 55 and 95?

Accepted Answer

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

Quiz 6: The Normal Distribution and Other Continuous Distributions

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes. What is the probability that a randomly chosen arrival to be more than 18 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 between 16 and 21 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. So, 70% of the products would be assembled within ______ minutes.

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour. What is the probability that a randomly chosen arrival to be more than 2.5 hours?

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes. What is the probability that a randomly chosen arrival to be less than 15 minutes?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour. What is the probability that a randomly chosen arrival to be more than 1 hour?

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 90 and 95?

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

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 standard deviation of the time interval?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of So 96% of the possible Z values are between and (symmetrically distributed about the mean).

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be between 121 and 124 inches?

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 55 and 95?

Quiz 6: The Normal Distribution and Other Continuous Distributions

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes. What is the probability that a randomly chosen arrival to be more than 18 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 between 16 and 21 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. So, 70% of the products would be assembled within ______ minutes.

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour. What is the probability that a randomly chosen arrival to be more than 2.5 hours?

Patients arriving at an outpatient clinic follow an exponential distribution with mean 15 minutes. What is the probability that a randomly chosen arrival to be less than 15 minutes?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour. What is the probability that a randomly chosen arrival to be more than 1 hour?

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 90 and 95?

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

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 standard deviation of the time interval?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of So 96% of the possible Z values are between ______ and ______ (symmetrically distributed about the mean).

The true length of boards cut at a mill with a listed length of 10 feet is normally distributed with a mean of 123 inches and a standard deviation of 1 inch. What proportion of the boards will be between 121 and 124 inches?

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 55 and 95?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of So 96% of the possible Z values are between and (symmetrically distributed about the mean).