MATH221 Week 5 Quiz (July 2019)

MATH 221 Statistics for Decision Making

Week 5 Quiz

Question 1(CO 3) Consider the following table:

Age Group Frequency

18-29 983

30-39 784

40-49 686

50-59 632

60-69 541

70 and over 527

If you created the probability distribution for these data, what would be the probability of 30-39?

0.165

0.237

0.425

0.189

Question 2(CO 3) Consider the following table of hours worked by part-time employees. These employees must work in 5 hour blocks.

Weekly hours worked Probability

5 0.06

15 0.61

20 0.18

25 0.15

Find the mean of this variable.

12.20

17.50

18.95

16.80

Question 3(CO 3) Consider the following table.

Defects in batch Probability

0 0.30

1 0.28

2 0.21

3 0.09

4 0.08

5 0.04

Find the variance of this variable.

1.49

0.67

1.41

1.99

Question 4(CO 3) Consider the following table:

Defects in batch Probability

0 0.21

1 0.28

2 0.30

3 0.09

4 0.08

5 0.04

Find the standard deviation of this variable.

1.33

1.67

1.78

1.41

Question 5(CO 3) Twenty-two percent of US teens have heard of a fax machine. You randomly select 12 US teens. Find the probability that the number of these selected teens that have heard of a fax machine is exactly six (first answer listed below). Find the probability that the number is more than 8 (second answer listed below).

0.024, 0.001

0.993, 0.000

0.993, 0.024

0.024, 0.000

Question 6(CO 3) Ten rugby balls are randomly selected from the production line to see if their shape is correct. Over time, the company has found that 85.2% of all their rugby balls have the correct shape. If exactly 7 of the 10 have the right shape, should the company stop the production line?

Yes, as the probability of seven having the correct shape is not unusual

Yes, as the probability of seven having the correct shape is unusual

No, as the probability of seven having the correct shape is not unusual

No, as the probability of seven having the correct shape is unusual

Question 7(CO 3) A bottle of water is supposed to have 12 ounces. The bottling company has determined that 98% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 bottles has all bottles properly filled?

n=12, p=36, x=98

n=36, p=0.98, x=36

n=36, p=0.98, x=12

n=0, p=0.98, x=36

Question 8(CO 3) On the production line the company finds that 95.6% of products are made correctly. You are responsible for quality control and take batches of 30 products from the line and test them. What number of the 30 being incorrectly made would cause you to shut down production?

Less than 26

Less than 28

Less than 27

More than 25

Question 9(CO 3) The probability of someone ordering the daily special is 52%. If the restaurant expected 65 people for lunch, how many would you expect to order the daily special?

34

35

30

31

Question 10(CO 3) Fifty-seven percent of employees make judgements about their co-workers based on the cleanliness of their desk. You randomly select 8 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual?

0, 1, 8

1, 2, 8

1, 2, 8

0, 1, 2, 8

Question 11(CO 3) Seventy-three percent of products come off the line ready to ship to distributors. Your quality control department selects 12 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired?

Fewer than 6

Fewer than 4

Fewer than 5

Fewer than 10

Question 12(CO 3) Out of each 100 products, 96 are ready for purchase by customers. If you selected 27 products, what would be the expected (mean) number that would be ready for purchase by customers?

27

0.96

26

96

Question 13(CO 3) Sixty-seven percent of adults have looked at their credit score in the past six months. If you select 31 customers, what is the probability that at least 20 of them have looked at their score in the past six months?

0.450

0.550

0.142

0.692

Question 14(CO 3) One out of every 92 tax returns that a tax auditor examines requires an audit. If 50 returns are selected at random, what is the probability that less than 3 will need an audit?

0.9978

0.0109

0.9828

0.0151

Question 15(CO 3) Thirty-eight percent of consumers prefer to purchase electronics online. You randomly select 16 consumers. Find the probability that the number who prefer to purchase electronics online is at most 5.

0.211

0.789

0.180

0.391

Question 16 (CO 3) The speed of cars on a stretch of road is normally distributed with an average 51 miles per hour with a standard deviation of 5.9 miles per hour. What is the probability that a randomly selected car is violating the speed limit of 50 miles per hour?

0.50

0.43

0.51

0.57

Question 17(CO 3) A survey indicates that shoppers spend an average of 22 minutes with a standard deviation of 16 minutes in your store and that these times are normally distributed. Find the probability that a randomly selected shopper will spend less than 20 minutes in the store.

0.20

0.37

0.45

0.55

Question 18(CO 3) The monthly utility bills in a city are normally distributed with a mean of $128 and a standard deviation of $23. Find the probability that a randomly selected utility bill is between $110 and $130.

0.318

0.316

0.783

0.217

Question 19(CO 3) A restaurant serves hot chocolate that has a mean temperature of 175 degrees with a standard deviation of 8.1 degrees. Find the probability that a randomly selected cup of hot chocolate would have a temperature of less than 164 degrees. Would this outcome warrant a replacement cup (meaning that it would be unusual)?

Probability of 0.09 and would not warrant a refund

Probability of 0.91 and would not warrant a refund

Probability of 0.09 and would warrant a refund

Probability of 0.91 and would warrant a refund

Question 20(CO 3) The yearly amounts of carbon emissions from cars in Belgium are normally distributed with a mean of 13.9 gigagrams per year and a standard deviation of 9.2 gigagrams per year. Find the probability that the amount of carbon emissions from cars in Belgium for a randomly selected year are between 12.8 gigagrams and 14.0 gigagrams per year.

0.519

0.052

0.452

0.548

Question 21(CO 3) On average, the parts from a supplier have a mean of 97.5 inches and a standard deviation of 12.2 inches. Find the probability that a randomly selected part from this supplier will have a value between 85.3 and 109.7 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?

Probability is 0.05, which is inconsistent with the Empirical Rule

Probability is 0.68, which is consistent with the Empirical Rule

Probability is 0.95, which is consistent with the Empirical Rule

Probability is 0.68, which is inconsistent with the Empirical Rule

Question 22(CO 3) A process is normally distributed with a mean of 104 rotations per minute and a standard deviation of 8.2 rotations per minute. If a randomly selected minute has 80 rotations per minute, would the process be considered in control or out of control?

Out of control as this one data point is more than three standard deviations from the mean

In control as only one data point would be outside the allowable range

Out of control as this one data point is more than two standard deviations from the mean

In control as this one data point is not more than three standard deviations from the mean

Question 23 (CO 3) The soup produced by a company has a salt level that is normally distributed with a mean of 5.4 grams and a standard deviation of 0.3 grams. The company takes readings of every 10th bar off the production line. The reading points are 5.8, 5.9, 4.9, 5.2, 5.0, 4.9, 6.2, 5.1, 6.7, 6.1. Is the process in control or out of control and why?

It is in control as the data points more than 2 standard deviations from the mean are far apart

It is in control as the values jump above and below the mean

It is out of control as one of these data points is more than 3 standard deviations from the mean

It is out of control as two of these data points are more than 2 standard deviations from the mean

Question 24(CO 3) The blenders produced by a company have a normally distributed life span with a mean of 8.2 years and a standard deviation of 1.3 years. What warranty should be provided so that the company is replacing at most 6% of their blenders sold?

6.9 years

9.5 years

6.2 years

10.2 years

Question 25(CO 3) A puck company wants to sponsor the players with the 10% quickest goals in hockey games. The times of first goals are normally distributed with a mean of 8.54 minutes and a standard deviation of 4.91 minutes. How fast would a player need to make a goal to be sponsored by the puck company?

14.83 minutes

7.92 minutes

9.16 minutes

2.25 minutes

Question 26(CO 3) A stock’s price fluctuations are approximately normally distributed with a mean of $104.50 and a standard deviation of $23.62. You decide to purchase whenever the price reaches its lowest 20% of values. What is the most you would be willing to pay for the stock?

$124.38

$98.52

$110.48

$84.62

Question 27(CO 3) The times that customers spend in a book store are normally distributed with a mean of 39.5 minutes and a standard deviation of 9.4 minutes. A random sample of 25 customers has a mean of 36.1 minutes or less. Would this outcome be considered unusual, so that the store should reconsider its displays?

Yes, the probability of this outcome at 0.035, would be considered unusual, so the display should be redone

No the probability of this outcome at 0.359 would be considered usual, so there is no problem

Yes, the probability of this outcome at 0.965 would be considered unusual, so the display should be redone

No, the probability of this outcome at 0.035, would be considered usual, so there is no problem

Question 28(CO 3) The weights of ice cream cartons are normally distributed with a mean weight of 20 ounces and a standard deviation of 0.5 ounces. You randomly select 25 cartons. What is the probability that their mean weight is greater than 20.06 ounces?

0.274

0.726

0.452

0.548

Question 29(CO 3) Recent test scores on the Law School Admission Test (LSAT) are normally distributed with a mean of 162.4 and a standard deviation of 15.9. What is the probability that the mean of 12 randomly selected scores is less than 161?

0.465

0.380

0.620

0.535

Question 30(CO 3) The mean annual salary for intermediate level executives is about $74000 per year with a standard deviation of $2000. A random sample of 36 intermediate level executives is selected. What is the probability that the mean annual salary of the sample is between $71000 and $73500?

0.334

0.067

0.933

0.885