# Project #15604 - Statistics, Probabilites

YOU MUST SHOW WORK FOR EVERY PROBLEM WITH A CALCULATION

SHOWING WHAT YOU PLUGGED INTO THE CALCULATOR IS SHOWING YOUR WORK

1. (8 pts) Answer each part and give a brief explanation for each answer.

a) If P(A)=0.32, what is the value of P(not A)?

b) If P(not aA) = 2/9, what is the value of P(A)?

c) Is it possible that P(A)=32/31

d) Is it possible that P(A) = 49/50

2. (4 pts) a) Create a sample space for all of the possible outcomes when tossing 3 coins (similar to the margin table on page 143 of the textbook).

b) Assign probabilities to each possible outcome in the sample space from part a, creating a probability space.

3. (4 pts) Calculate the odds of an event occurring when the probability of the event occurring is 25%.

4. (3 pts) You draw one card from a standard deck of 52 cards.  What is the probability that the card is the king of diamonds or the five of clubs?

5. (8 pts) Refer to the information for homework problems 33 through 38 in section 4.3 in the textbook which was about results for marijuana drug testing.  Among 143 subjects with positive test results, there are 24 false positives, and among 157 negative test results, there are 3 false negatives.

a) How many subjects are included in the study?

b) How many subjects did use marijuana?

c) What is the probability that a randomly selected subject did use marijuana?

d) What is the probability that a randomly selected subject tested positive or did use marijuana?

6. (3 pts) State whether the events are either independent or dependent and explain your answer.

Randomly selecting a consumer who owns a computer.

Randomly selecting a consumer who uses the Internet.

7. (4 pts) You draw two cards from a standard deck of 52 cards and do not replace the first card before you draw the second.  What is the probability that the first card is the king of diamonds and the second card is the five of clubs?

Problems 8 and 9 refer to the following situation:  The following table shows how 758 people applying for a credit card were classified according to home ownership and length of time in present job.

 Less than 2 years 2 or more years Row Total Owner 120 247 367 Renter 231 160 391 Column Total 351 407 758

8. (2 pts) If an applicant is selected at random, find the probability that the applicant has been in their present job for 2 or more years.

9. (2 pts) If an applicant is selected at random, find the probability that the applicant has been in their present job for less than 2 years, given that the applicant is a home-owner.

10. (4 pts) Identify each of the following random variables as continuous or discrete:

a) The time in hours that you sleep on a random weekday night.

b) The score on your final exam.

c) The number of stars in the sky.

d) The volume of paint in a bucket.

11. (6 pts) Given the following probability distribution, find its mean and standard deviation.  The random variable x represents the number of cups or cans of caffeinated beverages consumed by Americans each day.

 x P(x) 0 0.22 1 0.16 2 0.21 3 0.16 4 0.25

Problems 12 and 13 refer to the following situation:  It is claimed that 65% of the cars on the Valley Highway are going faster than the 65 mph speed limit.  A random sample of 25 cars was observed under normal driving conditions with no police car in sight.

12. (3 pts) What is the probability that all of the 25 cars were going faster than 65 mph?

13. (3 pts) What is the probability that fewer than ten of the cars were going over 65 mph?

14. (4 pts) Use the formula for the binomial distribution to find the probability of getting exactly 14 tails when a fair coin is flipped 29 times.

Problems 15 and 16 refer to the following information:  A biologist has found that 42% of all brown bears are infected with trichinosis.

15. (4 pts) a) What is the expected number of infected brown bears in a random sample of 22 brown bears?

b) What is the standard deviation of the number of infected brown bears in a random sample of 22 brown bears?

16. (3 pts) Calculate the minimum usual value and the maximum usual value for the number of infected brown bears.

17. (6 pts) Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1°C.  A thermometer is randomly selected and read.  For each of the following, sketch a normal distribution for the situation, and then find the probability that:

a) The thermometer reading is greater than -0.5°C

b) The thermometer reading is between -2.37°C and 1.1°C.

18. (4 pts) Find z critical value so that 5.2% of the standard normal curve lies to the right of z.

Problems 19 and 20 refer to the following situation:  Lewis earned 86 on his biology midterm and 82 on his history midterm.  In the biology class the mean score was 79 with standard deviation 6 and in the history class the mean score was 76 with standard deviation 4.

19. (4 pts) Convert each score to a standard z score.

20. (3 pts) On which of the two tests did Lewis do better when compared to the rest of the class?  Why?

Problems 21 through 23 refer to the following situation:  Researchers at a pharmaceutical company have found that the effective time duration of a safe dosage of a pain relief drug is normally distributed with mean 2 hours and standard deviation 0.3 hour.

21. (3 pts) For a patient selected at random, what is the probability that the drug will be effective for 3 hours or more?

22. (4 pts) For a random sample of 22 patients, what is the probability that the drug will be effective for 3 hours or more?

23. (3 pts) Why can the central limit theorem be used to calculate problem number 24 even though the sample size does not exceed 30?

24. (8 pts) Use your calculator to construct a normal quantile plot for the following data set, make a sketch of the plot on the test paper, then explain what the plot tells you about the normality of the data set.

Gross Revenues of 35 Motion Pictures (in millions of dollars):

117, 5, 103, 66, 121, 116, 101, 100, 55, 104, 213, 34, 12, 290, 47, 10, 111, 100, 322, 19, 117, 48, 228, 47, 17, 373, 380, 118, 33, 114, 120, 101, 120, 234, 209

 Subject Mathematics Due By (Pacific Time) 10/30/2013 09:00 pm
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