Deck 7: The Normal and Other Continuous Distributions

Question 1

A company's manufacturing process uses 500 gallons of water at a time.A "scrubbing" machine then removes most of a chemical pollutant before pumping the water into a nearby lake.To meet federal regulations the treated water must not contain more than 80 parts per million (ppm.) of the chemical.The machine's output can be described by a normal model with standard deviation 4.2 ppm.The company's lawyers insist that not more than 2% of the treated water should be over the limit.To achieve this, to what mean should the company set the scrubbing machine?

A)80 ppm.
B)75 ppm.
C)71.374 ppm.
D)88.626 ppm.
E)69.459 ppm.

Answer 1

71.374 ppm.

Question 2

Suppose the time it takes for customer representatives to diagnose and fix computer problems is uniformly distributed from 10 to 120 minutes.What is the probability that it takes longer than 90 minutes to diagnose and fix a computer problem?

A)0.27
B)0.73
C)0.82
D)0.50
E)0.18

Answer 2

0.27

Question 3

On weekdays from 11: 30 am to 2:00 pm customers arrive at a hotdog street vendor at the rate of 25 per 30 minute interval.Assume that this process can be well modeled by the Poisson distribution.What is the probability that the vendor will have to wait at least 3 minutes for a customer?

A)0.9179
B)0.6734
C)0.0821
D)0.3912
E)0.8854

Answer 3

0.0821

Question 4

At a local manufacturing plant, employees must complete new machine set ups within 30 minutes.New machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes.The typical worker needs five minutes to adjust to his or her surroundings before beginning duties.What percent of new machine set ups are completed within 25 minutes to allow for this?

A)77.3%
B)27.3%
C)22.7%
D)72.7%
E)none of the above

Question 5

On weekdays from 11: 30 am to 2:00 pm customers arrive at a hotdog street vendor at the rate of 25 per 30 minute interval.Assume that this process can be well modeled by the Poisson distribution.What is the average time between customer arrivals?

A)1.2 minutes
B)0.833 minutes
C)25 minutes
D)0.04 minutes
E)2 minutes

Question 6

A small flower shop takes orders by phone and then one of the staff florists is assigned to prepare the arrangement.The time it takes to process phone orders is normally distributed with a mean of 6 minutes and a standard deviation of 2.5 minutes.The time it takes for an arrangement to be completed is normally distributed with a mean of 35 minutes and a standard deviation of 8.6 minutes.What is the probability that it will take more than 50 minutes to process a phone order and complete the floral arrangement at this flower shop?

A)0.8413
B)0.3413
C)0.2167
D)0.1587
E)0.6843

Question 7

According to the Census Bureau, 64.5% of Americans owned their own home in 2013.A local real estate office wants to see if this is the case for its area.The office selects a random sample of 200 people to estimate the percentage who own their own homes.The standard deviation of the Normal model used to approximate this distribution is ________________________ .

A)136
B)64
C)27.07
D)6.767
E)3.384

Question 8

A small flower shop takes orders by phone and then one of the staff florists is assigned to prepare the arrangement.The time it takes to process phone orders is normally distributed with a mean of 6 minutes and a standard deviation of 2.5 minutes.The time it takes for an arrangement to be completed is normally distributed with a mean of 35 minutes and a standard deviation of 8.6 minutes.What is the standard deviation for the total time to process a phone order and complete the floral arrangement at this flower shop (assuming times are independent)?

A)8.96 minutes
B)41 minutes
C)80.28 minutes²
D)4.87 minutes
E)12.43 minutes

Question 9

The time it takes to process phone orders in a small florist/gift shop is normally distributed with a mean of 6 minutes and a standard deviation of 1.24 minutes.What cutoff value would separate the 2.5% of orders that take the most time to process?

A)3.52 minutes
B)4.76 minutes
C)8.48 minutes
D)10.01 minutes
E)11.98 minutes

Question 10

Suppose the time it takes for customer representatives to diagnose and fix computer problems is uniformly distributed from 10 to 120 minutes.What is the probability that a problem is diagnosed and fixed within 30 minutes?

A)0.27
B)0.73
C)0.82
D)0.50
E)0.18

Question 11

The unemployment rate of persons with a disability is typically higher than for those with no disability.Recent statistics report that this rate is 14.5%.An advocacy group in a large city located in the southeastern region of the U.S.selected a random sample of 250 persons with a disability.What is the probability that at least 20 persons in this sample are unemployed?

A)0.8686
B)0.9982
C)0.6573
D)0.1314
E)0.0018

Question 12

Based on data collected from its production processes, Crosstiles Inc.determines that the breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a standard deviation of 12.5 pounds per square inch.Based on the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking strengths between 375 and 425 pounds per square inch?

A)95%
B)68%
C)84%
D)32%
E)47.5%

Question 13

According to the Census Bureau, 64.5% of Americans owned their own home in 2013.A local real estate office wants to see if this is the case for its area.The office selects a random sample of 200 people to estimate the percentage who own their own homes.What is the probability that at least 140 people own their own home?

A)0.7291
B)0.052
C)0.4598
D)0.5402
E)0.104

Question 14

The unemployment rate of persons with a disability is typically higher than for those with no disability.Recent statistics report that this rate is 13.4%.An advocacy group in a large city located in the southeastern region of the U.S.selected a random sample of 250 persons with a disability.What is the probability that no more than 30 persons in this sample are unemployed?

A)0.7422
B)0.9982
C)0.5156
D)0.2578
E)0.0018

Question 15

At a local manufacturing plant, employees must complete new machine set ups within 30 minutes.New machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes.What percent of new machine set ups take more than 30 minutes?

A)97.72%
B)47.72%
C)2.28%
D)52.28%
E)none of the above

Question 16

Suppose that the time for e-mail confirmation of an online purchase is uniformly distributed between 1 and 6 minutes.The probability that an e-mail confirmation arrives within 3 minutes is ________________________ .

A)0.50
B)0.40
C)0.60
D)0.80
E)0.10

Question 17

The time it takes to process phone orders in a small florist/gift shop is normally distributed with a mean of 6 minutes and a standard deviation of 1.24 minutes.What cutoff values would separate the 16% of orders that take the least time to process?

A)3.52 minutes
B)4.76 minutes
C)8.48 minutes
D)10.01 minutes
E)11.98 minutes

Question 18

A company's manufacturing process uses 500 gallons of water at a time.A "scrubbing" machine then removes most of a chemical pollutant before pumping the water into a nearby lake.To meet federal regulations the treated water must not contain more than 80 parts per million (ppm) of the chemical.Because a fine is charged if regulations are not met, the company sets the machine to attain an average of 75 ppm in the treated water.The machine's output can be described by a normal model with standard deviation 4.2 ppm.What percent of the batches of water discharged exceed the 80 ppm standard?

A)11.7%
B)1.17%
C)88.3%
D)8.83%
E)3.89%

Question 19

Based on data collected from its production processes, Crosstiles Inc.determines that the breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a standard deviation of 12.5 pounds per square inch.Based on the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch?

A)95%
B)68%
C)16%
D)32%
E)47.5%

Question 20

Suppose that the time for e-mail confirmation of an online purchase is uniformly distributed between 1 and 6 minutes.What is the average time for an e-mail confirmation?

A)3 minutes
B)4 minutes
C)2.5 minutes
D)4.5 minutes
E)3.5 minutes