Question

Question 12 pts

The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly selected individual will take less than 6 minutes to select a shoe purchase. Is this outcome unusual?

Group of answer choices

Probability is 0.88, which is usual as it is greater than 5%

Probability is 0.12, which is usual as it is not less than 5%

Probability is 0.88, which is unusual as it is greater than 5%

Probability is 0.12, which is unusual as it is less than 5%

Question 22 pts

Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. Find the probability that a randomly selected bill will have an amount greater than $165, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?

Group of answer choices

Probability is 0.04, which is unusual as it is less than 5%

Probability is 0.04, which is usual as it is less than 5%

Probability is 0.96, which is unusual as it is greater than 5%

Probability is 0.96, which is usual as it is greater than 5%

Question 32 pts

In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 35 and 48 minutes on the treadmill.

Group of answer choices

-0.19

0.19

0.81

0.62

Question 42 pts

A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.84mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.24mm. Would this outcome warrant a refund (meaning that it would be unusual)?

Group of answer choices

Probability of 0.04 and would not warrant a refund

Probability of 0.96 and would warrant a refund

Probability of 0.04 and would warrant a refund

Probability of 0.96 and would not warrant a refund

Question 52 pts

A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than 10 minutes, the customer will be upset. Find the probability that a randomly selected customer takes more than 10 minutes if the average is 7.45 minutes with a standard deviation of 1.04 minutes.

Group of answer choices

0.007

0.501

0.993

0.071

Question 62 pts

In an agricultural study, the average amount of corn yield is normally distributed with a mean of 185.2 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 190 bushels of corn per acre?

Group of answer choices

282 acres

581 acres

503 acres

419 acres

Question 72 pts

On average, the parts from a supplier have a mean of 35.8 inches and a standard deviation of 2.4 inches. Find the probability that a randomly selected part from this supplier will have a value between 28.6 and 43.0 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?

Group of answer choices

Probability is 0.05, which is inconsistent with the Empirical Rule

Probability is 0.997, which is inconsistent with the Empirical Rule

Probability is 0.997, which is consistent with the Empirical Rule

Probability is 0.95, which is inconsistent with the Empirical Rule

Question 82 pts

A process is normally distributed with a mean of 10.2 hits per minute and a standard deviation of 1.04 hits. If a randomly selected minute has 12.9 hits, would the process be considered in control or out of control?

Group of answer choices

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

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

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

Question 92 pts

The candy produced by a company has a sugar level that is normally distributed with a mean of 16.8 grams and a standard deviation of 0.9 grams. The company takes readings of every 10^th bar off the production line. The reading points are 17.3, 14.9, 18.8, 16.5, 16.1, 17.4, 19.4. Is the process in control or out of control and why?

Group of answer choices

It is in control as none of these data points is more than 3 standard deviations from the mean

It is out of control as the values jump above and below the mean

It is out of control as at least two of three consecutive data points are more than 2 standard deviations from the mean

It is in control as at least two of three consecutive data points are more than 2 standard deviations from the mean

Question 102 pts

The toasters produced by a company have a normally distributed life span with a mean of 5.8 years and a standard deviation of 0.9 years, what warranty should be provided so that the company is replacing at most 3% of their toasters sold?

Group of answer choices

4.3 years

6.2 years

5.7 years

4.1 years

Question 112 pts

A running shoe company wants to sponsor the fastest 3% of runners. You know that in this race, the running times are normally distributed with a mean of 6.8 minutes and a standard deviation of 0.37 minutes. How fast would you need to run to be sponsored by the company?

Group of answer choices

6.2 minutes

7.4 minutes

6.1 minutes

7.5 minutes

Question 122 pts

The weights of bags of peas are normally distributed with a mean of 12.08 ounces and a standard deviation of 1.03 ounces. Bags in the upper 5% are too heavy and must be repackaged. What is the most that a bag can weigh and not need to be repackaged?

Group of answer choices

10.06 ounces

10.28 ounces

10.39 ounces

13.77 ounces

Question 132 pts

A stock’s price fluctuations are approximately normally distributed with a mean of $29.51 and a standard deviation of $3.87. You decide to sell whenever the price reaches its highest 10% of values. What is the highest value you would still hold the stock?

Group of answer choices

$34.47

$24.55

$33.38

$30.00

Question 142 pts

In a survey of first graders, their mean height was 49.9 inches with a standard deviation of 3.15 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students?

Group of answer choices

52.02 inches

46.75 inches

43.60 inches

47.77 inches

Question 152 pts

Hospital waiting room times are normally distributed with a mean of 38.12 minutes and a standard deviation of 8.63 minutes. What is the shortest wait time that would still be in the worst 10% of wait times?

Group of answer choices

46.75 minutes

27.06 minutes

49.18 minutes

29.49 minutes

Question 162 pts

A machine set to fill soup cans with a mean of 20 ounces and a standard deviation of 0.11 ounces. A random sample of 15 cans has a mean of 20.04 ounces. Should the machine be reset?

Group of answer choices

Yes, the probability of this outcome at 0.080, would be considered unusual, so the machine should be reset

No the probability of this outcome at 0.358 would be considered usual, so there is no problem

No, the probability of this outcome at 0.080, would be considered usual, so there is no problem

Yes, the probability of this outcome at 0.920 would be considered unusual, so the machine should be reset

Question 172 pts

The length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches. In a random sample of 45 boards, what is the probability that the mean of the sample will be between 94.5 inches and 95.1 inches?

Group of answer choices

0.009

0.408

0.591

0.901

Question 182 pts

The Dow Jones Industrial Average has had a mean gain of 432 pear year with a standard deviation of 722. A random sample of 40 years is selected. What is the probability that the mean gain for the sample was between 250 and 500?

Group of answer choices

0.137

0.863

0.669

0.331

Question 192 pts

Of all the companies on the New York Stock Exchange, profits are normally distributed with a mean of $6.54 million and a standard deviation of $10.45 million. In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between 0 million and 5.1 million?

Group of answer choices

0.105

0.012

0.120

0.015

Question 202 pts

Doing research for insurance rates, it is found that those aged 30 to 49 drive an average of 38.7 miles per day with a standard deviation of 6.7 miles. These distances are normally distributed. If a group of 60 drivers in that age group are randomly selected, what is the probability that the mean distance traveled each day is between 32.5 miles and 40.5 miles?

Group of answer choices

0.981

0.900

0.429

0.917

Answer 1

1)

Let X denote the length of time a person takes to decide which shoes to purchase (in minutes).

Then

X ~ N(u = 8.21, 0% = 1.904)

Required probability =

P(X < 6) = P(Z < 6 – 8.21 0.2-) = P(Z < -1.16) = P(Z > 1.16) 1.90

= 1- Plz<1.16) = 1-0.87698 = 0.12302 0.12

which is usual as it is not less than 5%.

Hence 2nd option is the correct option.