# Suppose x is a normal random variable with mean 60 and standard deviation 2. A z score was calculated

August 30, 2017

Question
Suppose x is a normal random variable with mean 60 and standard deviation 2. A z score was calculated for a number, and the z score is -1.3. What is x?

58.7

61.3

62.6

57.4

54.7

QUESTION 2

The length of time it takes for Gandolf’s fireworks to explode after they are launched is presumed to be uniformly distributed. If the length of time it takes them to explode occurs over the interval of 10 to 25 seconds, inclusive, then what is the probability that it will take less than 20 seconds for one to explode after it is launched?

0.40

0.67

1.00

0.80

QUESTION 3

The length of time it takes for Gandolf’s fireworks to explode after they are launched is presumed to be uniformly distributed. If the length of time it takes them to explode occurs over the interval of 10 to 25 seconds, inclusive, then what is the probability that it will take BETWEEN 20 and 22 seconds for one to explode after it is launched?

0.08

0.88

0.13

0.20

QUESTION 4

A carload of steel rods has arrived at Cybermatic Construction Company. The car contains 50,000 rods. Claude Ong, manager of Quality Assurance, directs his crew measure the lengths of 100 randomly selected rods. If the population of rods has a mean length of 120 inches and a standard deviation of 0.05 inch, the probability that Claude’s sample has a mean greater than 120.0125 inches is ___________ .

0.0124

0.0062

0.4938

0.9752

1.0000

QUESTION 5

A plant manager knows that the number of boxes of supplies received weekly is normally distributed with a mean of 200 and a standard deviation of 20. What percentage of the time will the number of boxes received weekly be greater than 200

100%

25%

0%

50%

QUESTION 6

A set of final examination grades in a calculus course was found to be normally distributed with a mean of 69 and a standard deviation of 9.

What is the probability of getting a grade of 91 or less on this exam?

1.00

0.50

0.0073

.9927

QUESTION 7

During the past six months, 73.2% of US households purchased sugar. Assume that these expenditures are approximately normally distributed with a mean of \$8.22 and a standard deviation of \$1.10.

Find the probability that a household spent less than \$5.00

.9983

0.000

1.00

0.0017

QUESTION 8

Given the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it:

No less than 55 feet?

.8413

.1587

.6826

.3174

QUESTION 9

If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is more than 0.89?

0.1064

0.2700

0.3936

0.6064

0.9000

QUESTION 10

Suppose a population has a mean of 90 and a standard deviation of 28. If a random sample of size 49 is drawn from the population, the probability of drawing a sample with a mean of less than 84 is _________ .

0.9332

0.0668

0.4332

0.8664

1.0000

QUESTION 11

Suppose the distribution of personal daily water usage in New York City is normally distributed with a mean of 15 gallons and a variance of 25 gallons. Because of a current problem with the distribution of water to its citizens, the mayor wants to give a city tax rebate to the 15 percent of the population who use the least amount of water. What should he use as the water limit for a person to qualify for a city tax rebate?

9.825

15.00

12.20

10.25

QUESTION 12

Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes. Suppose that in an effort to provide better service to the public, the director of the local office is permitted to provide discounts to those individuals whose waiting time exceeds a predetermined time. The director decides that 15% of the customers should receive this discount. What are the numbers of minutes they need to wait to receive the discount?

34.48

21.68

38.32

25.52

QUESTION 13

The chief chemist for a major oil/gasoline production company claims that the regular unleaded gasoline produced by the company contains on average 4 ounces of a certain ingredient. The chemist further states that the distribution of this ingredient per gallon of regular unleaded gasoline is normal and has a standard deviation of 1.2 ounces. What is the probability of finding an average in excess of 4.3 ounces of this ingredient from randomly inspected 100 gallons of regular unleaded gasoline?

.5987

.4013

.9938

.0062

QUESTION 14

The flying time of a drone airplane has a normal distribution with mean 4.76 hours and standard deviation of .04 hours. What is the probability that the drone will fly:

More than 4.80 hours?

.1587

.8413

.6587

3413

QUESTION 15

The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 13 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that no more than 40 accounts will be classified as delinquent?

42.07 %

92.07 %

7.93 %

40.15 %

90.15%

QUESTION 16

The net profit of an investment is normally distributed with a mean of \$10,000 and a standard deviation of \$5,000. The probability that the investor’s net gain will be at least \$5,000 is ___________ .

0.1859

0.3413

0.8413

0.4967

0.5000

QUESTION 17

The yearly cost of dental claims for the employees of the local shoe manufacturing company is normally distributed with a mean of \$105 and a standard deviation of \$35. What is the yearly cost at which 35% of the employees fall at or below?

\$118.48

\$127.29

\$82.71

\$91.53

QUESTION 18

While conducting experiments, a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m. What is the probability that a randomly selected depth is less than 3.60 m?

.72

.80

.46

.32

QUESTION 22

A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is

0

.0495

.4505

.9505

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