Prob & Stat



Prob & Stat Normal Curves

Part I. Find the area under the standard normal distribution for each. Use the table.

1. Between 0 and 1.41 2. Between 1.31 and 2.14

3. Between -2.1 and 0.03 4. To the right of z = -1.68

5. To the left of z = -0.6 6. To the left of 2.04

Part II. Using the standard normal distribution, find each probability. Use the table.

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Part III. Solve the following problems.

11. The average on a test is 84 with a standard deviation of 5 points. What is the probability that a person’s score is between 81 and 90?

12. The time it takes for a certain pain reliever to begin to reduce symptoms is 35 minutes, with a standard deviation of 3 minutes. Find the probability that it will take the medication

a. Between 30 and 32 minutes.

b. More than 36 minutes.

c. Between 36 and 39 minutes.

d. Less than 33 minutes.

13. If the average weight of a frog is 8.83 ounces and the standard deviation is 2.1 ounces, what is the probability that the mean weight of a frog will be more than 11.6 ounces?

11. An exclusive college desires to accept only the top 20% of all graduating seniors based on the results of a national placement test. This test has a mean of 500 and a standard deviation of 100. Find the cutoff score for the exam.

12. The average number of gallons of lemonade consumed by the football team during a game is 20, with a standard deviation of 3 gallons. When a game is played, find the probability of using

a. at most 21 gallons.

b. at least 22 gallons

c. Between 26 and 28 gallons.

13. A car dealer finds that the average price of a previously owned car is $8276. He decides to sell cars that well appeal to the middle 60% of the market in terms of price. Find the maximum and minimum prices of the cars the dealer will sell. The standard deviation if $1200.

14. The average American has 16 different jobs in their lifetime with a standard deviation of 4.3 jobs. The middle 55% of Americans will have somewhere between how many jobs?

15. MTV just piloted a new show called Extreme Polka Dancing. In order for the show to be picked up by the network, the pilot has to score in the top 33% of MTV’s new show viewer ratings. On average, MTV’s new shows score a 720 in the ratings with a standard deviation of 32. What rating does the pilot episode of Extreme Polka Dancing have to get in order to be picked up for circulation?

16. The average high school student swears 32 times in a school day with a standard deviation of 4.8 curse words. What is the probability that you will curse less than 20 times in one school day?

17. **Pizzas are delivered in 32 minutes on average with a standard deviation of 6.2 minutes. If 320 deliveries are randomly selected, how many of the pizzas will have been delivered in less than 20 minutes?**

Part IV. Find the mean and standard deviation of the following probability distribution.

21. Answer the following questions using the probability distribution below in which x is the number of students wearing coats.

a. Mean _________ b. St. Dev.________

c. Find the probability that the number of students wearing a coat is within two deviation of the mean.

Part V. Find the following using the binomial formula. Show all work.

22.A survey found that 82% of the students eat school lunch.

a. What is the probability that out of a group of fifteen students at most 12 eat school lunch.

b. What is the probability that exactly 13 in a group of fifteen students each school lunch?

Part VI. Solve using the graphing calculator binomial distribution feature.

________ 23. A survey found that 86% of Americans have never been a victim of violent crime. If a sample of 18 Americans is selected at random, find the probability that less than 12 have never been a victim of violent crime.

________24. In a survey, 58% of American adults said they had never heard of the Internet. If 20 American adults are selected at random, find the probability that at least 13 will say they had never heard of the Internet.

________ 25. In the past year, 13% of businesses have eliminated jobs. If five businesses are selected at random, find the probability that exactly three have eliminated jobs during the last year.

________ 26. Of graduating high school seniors, 14% said that their generation will be remembered for their social concerns. If seventeen graduating seniors are selected at random, find the probability that more than 3 will agree with that statement.

Part VII. Solve the following. Show all work – use appropriate formulas!

27. The school is planning on buying a new Xerox machine. The company has two payment options. The first option is $1200 with unlimited repairs. The second option is $1000 plus $50 per repair. The probability distribution for the number of repairs is given below. Find the mean of both plans and the standard deviation of both plans. Then choose the best plan and explain why you chose it.

Use the Following for #9-10.

In a recent study, the following data were obtained in response to the question, "Do you favor recycling in your neighborhood?".

________ 28. If a person is picked at random, what is the probability that the person is male or is against recycling?

________ 29. If a person is picked at random, what is the probability that the person did not respond “yes” to the question.

________ 30. If a person is picked at random, what is the probability that the person is a male given that they responded “no” to the question.

________ 31. A card is drawn and replaced, then a second card is drawn. What is the probability of getting 2 clubs?

________ 32. A club has 8 doctors, 10 engineers, and 12 lawyers. If a person is picked at random, what is the probability that he or she is not an engineer?

________ 33. Find P(Ace | Diamond)

________ 34. I have a bag with 6 red marbles and 4 blue marbles. What is the probability of drawing two red marbles if I replace the first one drawn?

________ 35. If I draw two cards from a regular deck of cards, what is the probability that the first is a king and the second is a queen if there is no replacement.

Use the following for #36-38.

A survey was taken among a group of people. The probability that a person has a land line phone in his house is 0.93, the probability that they own a cell phone is 0.71, and that probability that a person owns both a land line and a cell phone is 0.66.

________ 36. What is the probability that a person has at least one kind of phone?

________ 37. What is the probability that a person does not have a phone?

________ 38. What is the probability that if a person has a land line, he also has a cell phone?

________ 39. If I roll two dice, what is the probability getting a sum of 6 or 10.

________ 40. If P(A)= .25 and P(B) = .6 find P(A or B) if events A and B are mutually exclusive

___below_ 41. Determine if the following are independent or dependent.

P(A)= .6

P (B) = .2

P(A and B)= .12

________ 42. Three companies manufacture plastic rings. Company A manufactures 30% of the rings on the market, Company B makes 50% of the rings on the market and Company C makes the remaining 20%. Five percent of the rings from Company A are red and 4% from Company B are red, and 3% from Company C are red. If I have a red ring, what is the probability that it came from Company A?

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|x |0 |1 |2 |3 |4 |

|P(x) |0..23 |0.04 |0.31 |0.08 |0.65 |

|# repairs, x |0 |1 |2 |

|Males |40 |15 |5 |

|Females |30 |20 |10 |

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