Directions: Do all of your work on this answer sheet. If you must, you may include additional pages to this answer sheet; however, if you do not properly fill out this answer sheet your problems will not be graded. If you have any questions about this assignment, always feel free to ask your instructor.

* Page numbers are approximated due to version control of the eResources, especially for Illowsky et al.

**Week 4 Homework assignment problems. You are still responsible for reviewing the balance of problems as they will be used in the question pool for your future quizzes.

Conceptual Problems

Figure C – Probability function

C1: Using Figure C above, what is the probability P(x=12)?

1. 2
2. ½
3. 0
4. None of these

C2: Using Figure C above, what is the probability P(x≤5)

1. 1
2. 1/4
3. 15/20
4. None of these

C3: True or False: Using Figure C above, P(x>3|x>2) = P(x>3)?

C4: The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. Show work. See Illowsky p. 300 for help.

1. Find a and b and describe what they represent.
2. Write the distribution.
3. Find the mean and the standard deviation.
4. What is the probability that the duration of games for a team for the 2011 season is between 480 and 500 hours?
5. What is the 65th percentile for the duration of games for a team for the 2011 season?

Book Problems

Lane Chapter 7

Problem 8 (Use for 8A-D) Assume the speed of vehicles along a stretch of I-10 has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.

8A. The current speed limit is 65 mph. The proportion of vehicles less than or equal to the speed limit is most nearly which of the following?

1. 2498
2. 2266
3. 2673
4. 2123

8B. The proportion of vehicles going less than 50 mph is most nearly which of the following?

1. 0096
2. 0081
3. 0063
4. 0043

8C. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. The new speed limit based on this criterion is most nearly which of the following? Y

88. 00 mph
89. 25 mph
90. 25 mph
91. 46 mph

8D. In what way do you think the actual distribution of speeds differs from a normal distribution?

1. Positively skewed
2. Negatively skewed
3. No difference between the actual distribution and normal distribution.
4. What’s a distribution?

Problem 12 Use the normal distribution to approximate the binomial distribution and find the probability of getting 15 to 18 heads out of 25 flips. Compare this to what you get when you calculate the probability using the binomial distribution. Write your answers out to four decimal places. Compute each probability to four (4) decimal place.

• Normal approximation: ___________

• Binomial: ___________

Illowsky Chapter 6

Problem 66 Height and weight are two measurements used to track a child’s development. The World Health Organization measures child development by comparing the weights of children who are the same height and the same gender. In 2009, weights for all 80 cm girls in the reference population had a mean µ = 10.2 kg and standard deviation σ = 0.8 kg. Weights are normally distributed. X ~ N (10.2, 0.8). Calculate the z-scores that correspond to the following weights and interpret them. Compute the z scores to three (3) decimal places (e.g. 1 à 1.000).

1. 11 kg             z score: __000____
2. 9 kg             z score: __-2.875___
3. 2 kg z score: __2.500____

Problem 88 (Use for 8A-B) Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site. On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent.

88A. Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30.

1. 4323
2. 3446
3. 3827
4. 4800

88B. Find the 95^th percentile, and express it in a sentence.

30. 00%
31. 23%
32. 22%
33. 43%

Illowsky Chapter 7

Problem 70. Which of the following is NOT TRUE about the distribution for averages?

1. The mean, median, and mode are equal.
2. The area under the curve is one.
3. The curve never touches the x-axis.
4. The curve is skewed to the right.

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