Question 1

Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.

Accepted Answer

The answer of Given that X is a normally distributed...

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 between 25 and 30 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

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, 60% of the products would be assembled within____ and ____minutes (symmetrically distributed about the mean).

Accepted Answer

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

Question 4

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, find the mean and standard deviation of John's total income from these two jobs for a given month.

Accepted Answer

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

Question 5

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with µ = 110 grams and ? = 25 grams. What is the probability that a randomly selected vitamin will contain between 100 and 110 grams of pyridoxine?

Accepted Answer

The answer of The amount of pyridoxine (in grams) in...

Question 6

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 second standard normal quantile is ______.

Accepted Answer

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

Question 7

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 less than 25 or more than 30 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 8

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 13 and 14 seconds?

Accepted Answer

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

Question 9

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 90?

Accepted Answer

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

Question 10

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1.5 patients per hour. What is the probability that a randomly chosen arrival to be less than 10 minutes?

Accepted Answer

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

Question 11

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 less than 124 inches?

Accepted Answer

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

Question 12

TABLE 6-1
The manager of a surveying company believes that the average number of phone surveys completed per hour by her employees has a normal distribution. She takes a sample of 15 days output from her employees and determines the average number of surveys per hour on these days. The ordered array for this data is: 10.0, 10.1, 10.3, 10.5, 10.7, 11.2, 11.4, 11.5, 11.7,
11.8, 11.8, 12.0, 12.2, 12.2, 12.5.
-Referring to Table 6-1, the fourth standard normal quantile is _____.

Accepted Answer

The answer of TABLE 6-1
The manager of a surveying company...

Question 13

TABLE 6-1
The manager of a surveying company believes that the average number of phone surveys completed per hour by her employees has a normal distribution. She takes a sample of 15 days output from her employees and determines the average number of surveys per hour on these days. The ordered array for this data is: 10.0, 10.1, 10.3, 10.5, 10.7, 11.2, 11.4, 11.5, 11.7,
11.8, 11.8, 12.0, 12.2, 12.2, 12.5.
-Referring to Table 6-1, the first standard normal quantile is ______ .

Accepted Answer

The answer of TABLE 6-1
The manager of a surveying company...

Question 14

A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces.

Accepted Answer

The answer of A food processor packages orange juice in...

Question 15

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with µ = 110 grams and ? = 25 grams. What is the probability that a randomly selected vitamin will contain between 100 and 120 grams of pyridoxine?

Accepted Answer

The answer of The amount of pyridoxine (in grams) in...

Question 16

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, the probability is 0.2 that John's total income from these two jobs in a given month is less than how much?

Accepted Answer

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

Question 17

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of So 27% of the possible Z values are smaller than _____.

Accepted Answer

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

Question 18

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 at least 80 minutes?

Accepted Answer

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

Question 19

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 more than 25 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 20

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

Accepted Answer

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

Quiz 6: The Normal Distribution and Other Continuous Distributions

Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 47 and 54.

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, 60% of the products would be assembled within and minutes (symmetrically distributed about the mean).

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with µ = 110 grams and ? = 25 grams. What is the probability that a randomly selected vitamin will contain between 100 and 110 grams of pyridoxine?

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 90?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1.5 patients per hour. What is the probability that a randomly chosen arrival to be less than 10 minutes?

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 less than 124 inches?

A food processor packages orange juice in small jars. The weights of the filled jars are approximately normally distributed with a mean of 10.5 ounces and a standard deviation of 0.3 ounce. Find the proportion of all jars packaged by this process that have weights that fall below 10.875 ounces.

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with µ = 110 grams and ? = 25 grams. What is the probability that a randomly selected vitamin will contain between 100 and 120 grams of pyridoxine?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of So 27% of the possible Z values are smaller than _____.

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