Question

1) Let x be a continuous random variable that is normally distributed with a mean of 21 and a standard deviation of 7. Find to 4 decimal places the probability that x assumes a value

a. between 24 and 30.

Probability =

b. between 17 and 31.

Probability =

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2) Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value less than 43.

Round your answer to four decimal places.

P=

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3) Let x denote the time taken to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race in 218 to 240 minutes?

Round your answer to four decimal places.

P=

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4) According to the records of an electric company serving the Boston area, the mean electric consumption for all households during winter is 1650 kilowatt-hours per month. Assume that the monthly electric consumptions during winter by all households in this area have a normal distribution with a mean of 1650 kilowatt-hours and a standard deviation of 320 kilowatt-hours. What percentage of the households in this area have a monthly electric consumption of 1836 to 1924 kilowatt-hours?

Round your answer to two decimal places.

P= _______%

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5) The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $110 and a standard deviation of $83.33. If the management decides to give free gifts to all those customers who spend more than $150 at this supermarket during a visit, what percentage of the customers are expected to get free gifts?

Round your answer to two decimal places.

_________% of the customers are expected to get free gifts.

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6) The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 6.0 ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of 5.76 ounces and a standard deviation of 0.15 ounces. What percentage of the pucks produced at this factory cannot be used by the National Hockey League?

Round your answer to two decimal places.

The percentage of pucks that cannot be used is__________ %.

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7) At Jen and Perry Ice Cream Company, the machine that fills 1-pound cartons of Top Flavor ice cream is set to dispense 16 ounces of ice cream into every carton. However, some cartons contain slightly less than and some contain slightly more than 16 ounces of ice cream. The amounts of ice cream in all such cartons have a normal distribution with a mean of 16 ounces and a standard deviation of 0.42 ounces. Find the probability that a randomly selected carton contains 16.187 to 16.194 ounces of ice cream.

Round your answer to four decimal places.

P= _____________

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8)

Two companies, A and B, drill wells in a rural area. Company A charges a flat fee of 3727 dollars to drill a well regardless of its depth. Company B charges 944 dollars plus 12 dollars per foot to drill a well. The depths of wells drilled in this area have a normal distribution with a mean of 230 feet and a standard deviation of 35 feet. Find the probability that Company B would charge more than Company A to drill a well.

Round your answer to four decimal places.

P= ____________

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9) The amount of time taken by a bank teller to serve a randomly selected customer has a normal distribution with a mean of 2 minutes and a standard deviation of 0.5 minutes. Find the probability that at least one of four randomly selected customers will need more than 2.25 minutes to be served.

Round your answer to four decimal places.

P=____________

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10)

The SCT is a standardized test with a known normal distribution having a mean of 18 and a standard deviation of 3.

a) What percentile would a score of 12 be? (choose from: 1st, 2nd, 3rd, 4th, 5th, 6th, 7th percentile)

b) What percentile would a score of 20 be? (choose from: 55th, 60th, 65th, 75th, 85th, 90th percentile)

c) What score corresponds to the 85^th percentile? Score = (choose from: 18,19,20,21,22,23,24,25)

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11) According to the U.S. Department of Agriculture, the average American consumed 54.3 pounds (approximately seven gallons) of salad and cooking oils in 2008 (www.ers.usda.gov/data/foodconsumption). Suppose that the current distribution of salad and cooking oil consumption is approximately normally distributed with a mean of 54.3 pounds and a standard deviation of 14.5 pounds.

Round your answers to two decimal places.

a. What percentage of Americans’ annual salad and cooking oil consumption is less than 10 pounds?

b. What percentage of Americans’ annual salad and cooking oil consumption is between 45 and 65 pounds?

c. What percentage of Americans’ annual salad and cooking oil consumption is more than 95 pounds?

d. What percentage of Americans’ annual salad and cooking oil consumption is between 55 and 75 pounds?

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12)

Let   x be a continuous random variable that follows a normal distribution with a mean of 321 and a standard deviation of 41.

(a) Find the value of   x > 321 so that the area under the normal curve from 321 to x is 0.2224.

Round your answer to the nearest integer.
The value of   x is_______

(b) Find the value of x so that the area under the normal curve to the right of x is 0.3745.

Round your answer to the nearest integer.
The value of   x is ______

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13) Fast Auto Service provides oil and lube service for cars. It is known that the mean time taken for oil and lube service at this garage is 15 minutes per car and the standard deviation is 2.4 minutes. The management wants to promote the business by guaranteeing a maximum waiting time for its customers. If a customer's car is not serviced within that period, the customer will receive a 50% discount on the charges. The company wants to limit this discount to at most 2% of the customers. What should the maximum guaranteed waiting time be? Assume that the times taken for oil and lube service for all cars have a normal distribution.

Round your answer to the nearest minute.

The maximum guaranteed waiting time should be approximately ___________ minutes.

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14) A study has shown that 24% of all college textbooks have a price of $80 or higher. It is known that the standard deviation of the prices of all college textbooks is $10.00. Suppose the prices of all college textbooks have a normal distribution. What is the mean price of all college textbooks?

Round your answer to the nearest integer.

μ=

Answer 1