# 0.1 Review exercises (ch 3-13)  (Page 4/12)

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Using the following information to answer the next two exercises: 64 faculty members were asked the number of cars they owned (including spouse and children’s cars). The results are given in the following graph:

36. Find the approximate number of responses that were three.

37. Find the first, second and third quartiles. Use them to construct a box plot of the data.

Use the following information to answer the next three exercises: [link] shows data gathered from 15 girls on the Snow Leopard soccer team when they were asked how they liked to wear their hair. Supposed one girl from the team is randomly selected.

Hair Style/Hair Color Blond Brown Black
Ponytail 3 2 5
Plain 2 2 1

38. Find the probability that the girl has black hair GIVEN that she wears a ponytail.

39. Find the probability that the girl wears her hair plain OR has brown hair.

40. Find the probability that the girl has blond hair AND that she wears her hair plain.

## Chapter 6

Use the following information to answer the next two exercises: X ~ U (3, 13)

41. Explain which of the following are false and which are true.

1. f ( x ) = $\frac{1}{10}$ , 3 ≤ x ≤ 13
2. There is no mode
3. The median is less than the mean.
4. P ( x >10) = P ( x ≤ 6)

42. Calculate:

1. the mean.
2. the median.
3. the 65 th percentile.

43. Which of the following is true for the box plot in [link] ?

1. Twenty-five percent of the data are at most five.
2. There is about the same amount of data from 4–5 as there is from 5–7.
3. There are no data values of three.
4. Fifty percent of the data are four.

44. If P ( G | H ) = P ( G ), then which of the following is correct?

1. G and H are mutually exclusive events.
2. P ( G ) = P ( H )
3. Knowing that H has occurred will affect the chance that G will happen.
4. G and H are independent events.

45. If P ( J ) = 0.3, P ( K ) = 0.63, and J and K are independent events, then explain which are correct and which are incorrect.

1. P ( J AND K ) = 0
2. P ( J OR K ) = 0.9
3. P ( J OR K ) = 0.72
4. P ( J ) ≠ P ( J | K )

46. On average, five students from each high school class get full scholarships to four-year colleges. Assume that most high school classes have about 500 students. X = the number of students from a high school class that get full scholarships to four-year schools. Which of the following is the distribution of X ?

1. P (5)
2. B (500, 5)
3. Exp $\left(\frac{1}{5}\right)$
4. $N\left(5,\frac{\left(0.01\right)\left(0.99\right)}{500}\right)$

## Chapter 7

Use the following information to answer the next three exercises: Richard’s Furniture Company delivers furniture from 10 A.M. to 2 P.M. continuously and uniformly. We are interested in how long (in hours) past the 10 A.M. start time that individuals wait for their delivery.

47. X ~ _________

1. U (0, 4)
2. U (10, 20)
3. Exp (2)
4. N (2, 1)

48. The average wait time is:

1. 1 hour.
2. 2 hours.
3. 2.5 hours.
4. 4 hours.

49. Suppose that it is now past noon on a delivery day. The probability that a person must wait at least 1.5 more hours is:

1. $\frac{1}{4}$
2. $\frac{1}{2}$
3. $\frac{3}{4}$
4. $\frac{3}{8}$

50. Given: X ~ Exp $\left(\frac{1}{3}\right)$

1. Find P ( x >1).
2. Calculate the minimum value for the upper quartile.
3. Find P $\left(x=\frac{1}{3}\right)$

51.

• 40% of full-time students took 4 years to graduate
• 30% of full-time students took 5 years to graduate
• 20% of full-time students took 6 years to graduate
• 10% of full-time students took 7 years to graduate

The expected time for full-time students to graduate is:
1. 4 years
2. 4.5 years
3. 5 years
4. 5.5 years

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x 0 1 2 3 4 5 0.05 0.09 0.17 0.27 0.23 0.19 a) Find the probability that 1 or 2 smart phones have defects (show calculations). b) Find the probability that more than 3 smart phones have defects (show calculations). c) Find the probability that at most 2 smart phones have defects (show calculat
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