# Module 4 homework

# Problem Set 4.4

1. Suppose that for a normal random variable X, we have a mean of µ=10 and a standard deviation of σ=3.

a) What is the probability that X will be less than 13?

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b) What is the probability that X will be less than 8?

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c) What is the probability that X will be greater than 12?

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d) What is the probability that X will be greater than 6?

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e) What is the probability that X will be between than 3 and 17?

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f) What is the probability that X will be between than 8 and 14?

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2. A farmer harvests several heads of iceberg lettuce. The weight of the heads of lettuce are normally distributed with a mean weight of 2.2 pounds and a standard deviation of .55 pounds. If you choose a head of lettuce at random, what is the probability that the head you chose will weigh:

a) Less than 2 pounds?

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b) Greater than 2.5 pounds?

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c) Between 1.8 pounds and 2.7 pounds?

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3. Suppose that the scores of a history test are normally distributed with a mean of 565 and a standard deviation of 113.

a) What percentage of the scores are less than 450?

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b) What percentage of the scores are greater than 500?

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c) What percentage of the scores are between 550 and 600?

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d) Suppose you pick an individual history test at random, what is the probability that the score on the test is between 575 and 625?

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4. The time that people stand in the waiting line at a particular fast food restaurant is normally distributed with a mean time of 130 seconds and a standard deviation of 25 seconds. If you go to that fast food restaurant, what is the probability that you will stand in the waiting line for:

a) More than 150 seconds?

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b) Less than 120 seconds?

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c) Between 110 seconds and 150 seconds?

– Click here to enter answer – . A convenience store sells between five and twelve boxes of sugar each week. The probabilities are given as follows:

Find the number of boxes of sugar that the convenience store should expect to sell per week. Also, find the variance and standard deviation of this data.

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2. A barber expects to get between zero and six customers per hour in his barber shop. The probability of these is given as follows:

Find the number of expected customers that the barber will get per hour. Also, find the variance and standard deviation of this data.

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3. A company makes bulbs for Christmas trees. Unfortunately, the boxes that contain the bulbs have been mishandled and many of the boxes contain one or more broken bulbs. The number of broken bulbs per box, along with the related probabilities are given as:

Find the expected number of broken bulbs per box.

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# Problem Set 4.2

1 . A basketball player makes foul shots 75 % of the time. If she takes 9 shots, what is the probability that she will make exactly 7 shots.

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2. A baseball player has a batting average of .211 (in other words, he gets a hit 21.1 % of the time that he goes up to bat). If he goes up to bat 13 times, what is the probability that he will get exactly 4 hits?

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3. A large shipment of light bulbs has just arrived at a store. It has been revealed that 17 % of the light bulbs are defective (the other light bulbs are good). Suppose that you choose 6 light bulbs at random. What is the probability that 2 or less of the bulbs are defective.

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4. Your factory has seven safety systems. During an emergency, the probability of any one of the safety systems failing is .06. The factory will be in danger if more than four safety systems fail. What is the probability of your factory being in danger during an emergency?

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# Problem Set 4.3

(Remember: You may find the standard normal table by clicking Help Files on the upper right of this page)

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