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• From Mathematics, Probability
• Due on 09 Apr, 2016 01:43:00
• Asked On 09 Apr, 2016 05:25:28
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At the Wilmington Trust Bank, on average 8 customers arrive per hour at the drive-through window. What is the probability that, in any hour, less than 8 will arrive? Round your answer to 4 decimals

0.4530

0.4457

0.4335

0.4318

5 points

Question 2

1. Use this table for the following question.

Supplier

Number Conforming

Number Nonconforming

A

101

3

B

95

6

C

36

2

What is the probability of that a randomly selected part will be from supplier B, or a nonconforming unit from supplier A, or a conforming part from supplier C?

0.6846

0.6620

0.5761

0.4854

5 points

Question 3

1. The number of cell phone minutes used by high school seniors during the school year follows a normal distribution with a mean of 625 and a standard deviation of 55. What is the probability that a student uses more than 575 minutes?

0.6475

0.8133

0.8186

0.8925

5 points

Question 4

1. On the basis of past experience, 26% of the bills of a large mail-order book company are incorrect. If a random sample of seven current bills is selected what is the probability that two or less are incorrect?

0.6475

0.7354

0.9730

0.9920

5 points

Question 5

1. Ford Motor Company is confident that its 2016 F-150 truck gets 26 miles per gallon on the highway. Before they begin to advertise this fact they want to be 98% certain of their claim. To accomplish this, they take a random sample of 250 trucks and measure their gas mileage. The average was 24.91 mpg with a population standard deviation of 4.77 mpg. Calculate the Upper and Lower Confidence Interval values AND can Ford make the claim that their trucks will get 26 mpg on the highway.

Lower = 25.06, Upper = 26.94 & Claim is yes their trucks do get 26 mpg

Lower = 24.38, Upper = 25.58 & Claim is no their trucks do not get 26 mpg

Lower = 24.21, Upper = 25.61, & Claim is no their trucks do not get 26 mpg

Lower = 24.19, Upper = 25.71, & Claim is no their trucks do not get 26 mpg

5 points

Question 6

1. The time required to complete a project is normally distributed with a mean of 110 weeks and a standard deviation of 13.65 weeks. The construction company must pay a penalty if the project is not finished by the due date in the contract. If a construction company bidding on this contract wishes to be 90 percent sure of finishing by the due date, what due date (project week #) should be negotiated?

112.39

120.96

124.08

127.49

5 points

Question 7

1. Customers arrive at a supermarket checkout counter with an average arrival rate of 9 customers per hour. What is the probability of less than 7 customers arriving at the supermarket checkout counter in a given one-hour period?

0.2068

0.1432

0.0998

0.0625

5 points

Question 8

1. A local commuter bus service advertises that buses run every eighteen minutes along a certain route. What is the probability of a bus picking up the passengers at a given bus stop in less than or equal to 15 minutes following their arrival at the bus stop? (Hint: Use the exponential distribution method to solve this question)

0.5709

0.5654

0.5831

0.5925

5 points

Question 9

1. If the average number of cars that passed through a toll both between 2:00 AM & 3:00 AM is sixteen, what is the probability that tonight exactly 19 cars would pass during the same time frame?

0.0418

0.0467

0.0699

0.0814

5 points

Question 10

1. If on average the customer service center receives 24 calls per hour during the hours of noon till 3:00 PM. What is the probability that today 20 or more calls will be received?

0.8197

0.8252

0.8310

0.8564

5 points

Question 11

1. The total expenses of a hospital are related to many factors. Two of these factors are the number of beds in the hospital, and the number of admissions. Data was collected on 8 hospitals as shown in the table below. Develop a regression model to predict the total expenses of a hospital based upon the number of beds.

Expenses

# Beds

1

61

220

2

131

341

3

161

525

4

28

140

5

18

40

6

97

215

7

49

145

8

10

95

Y = 0.339x - 3.516

Y = -15.64 – 1.02x

Y = 0.339x - 2.128

Y = .339x - 5.822

5 points

Question 12

1. The total expenses of a hospital are related to many factors. Two of these factors are the number of beds in the hospital, and the number of admissions. Data was collected on 8 hospitals as shown in the table below. Develop a regression model to predict the total expenses of a hospital based upon the number of admissions.

Expenses

1

61

81

2

131

164

3

161

230

4

28

47

5

18

13

6

97

159

7

49

57

8

10

7

Y = 0.671x + 9.284

Y = 5.426 + 0.675x

Y = 0.671x + 3.931

Y = .032x + 6.751

5 points

Question 13

1. The total expenses of a hospital are related to many factors. Two of these factors are the number of beds in the hospital, and the number of admissions. Data was collected on 8 hospitals as shown in the table below. Develop a regression model to predict the total expenses of a hospital based upon the number of beds and the number of admissions.

Expenses

# Beds

1

61

220

81

2

131

341

164

3

161

525

230

4

28

140

47

5

18

40

13

6

97

215

159

7

49

145

57

8

10

95

7

Y = 0.073X1 + 0.541X2 + 5.66

Y = 0.073X1 +0.541X2 + 0.593

Y = 1.02X1 -15.64X2 + 0.07

Y = 0.079X1 +0.533X2 + 1.85

5 points

Question 14

1. Refer to the data and your solutions to questions 11 – 13 and identify which of the three models best predicts the expenses of a hospital.

The regression model based upon beds only is the best because it has the highest r value.

The regression model based upon admissions only is the best because it has the highest r value.

The regression model based upon beds and admissions is the best because it has the highest r value.

The regression model based upon beds only is the best because it has the highest r2 value.

The regression model based upon admissions only is the best because it has the highest r2 value.

5 points

Question 15

1. Question 13 states: “The total expenses of a hospital are related to many factors. Two of these factors are the number of beds in the hospital, and the number of admissions.” Identify the F critical value for the regression model in Question 13.

6.608

5.786

5.318

4.459

5 points

Question 16

1. The owner of a bicycle repair and sales business has hired you to help him make his business more profitable. The following table shows sales data for one product for each month for the year (assume 30 days/month). These data will be referenced in order to answer questions 16 - 20.

Month

Sales

Forecast

Month 1

92

91

Month 2

77

Month 3

66

Month 4

74

Month 5

68

Month 6

84

Month 7

84

Month 8

74

Month 9

75

Month 10

63

Month 11

86

Month 12

84

Month 13

Question 16: Use a 4-month moving average to calculate the sales forecast for months 5, 10 & 13.

77.25, 79.25 & 77.00

77.50, 79.75 & 76.75

78.75, 81.00 & 78.25

81.97, 79.28 & 79.38

5 points

Question 17

1. Refer to the data in the Question 16 and use exponential smoothing at an alpha of 0.30 to calculate each month’s forecast. What are the forecasts for Months 4, 10 & 12

74.5, 75.75 & 77.5

80.92, 77.74 & 76.82

80.71, 77.16 & 76.84

81.97, 79.28 & 79.38

5 points

Question 18

1. Refer to the data in the Question 16 and calculate the seasonal index for Months 3 and 6.

0.85 & 1.08

0.85 & 1.09

0.85 & 1.02

0.83 & 1.06

5 points

Question 19

1. Refer to the data in the Question 16 and use the forecast generated by the exponential smoothing method calculate the MAD for the data.

9.29

8.86

8.19

4.62

5 points

Question 20

1. Refer to the data in the Question 16 and calculate the Weighted Average Forecast for Months 5 - 13 where the most recent month carries a weight of 4, the next most recent month a weight of 3, the next a weight of 2 and finally the oldest month carries a weight of 1. The weights are arranged from the most recent month to the oldest month: 4, 3, 2, & 1. What are the forecasts for months 6, 9 & 13?

71.2, 79.4 & 79.2

73.7, 81.9 & 81.0

75.2, 91.9 & 81.0

70.3, 78.4 & 79.5

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