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Review

Module by: Susan Dean, Barbara Illowsky, Ph.D.. E-mail the authors

Summary: This module provides a number of homework/review problems related to Continuous Random Variables.

Exercise 1Exercise 7 refer to the following study: A recent study of mothers of junior high school children in Santa Clara County reported that 76% of the mothers are employed in paid positions. Of those mothers who are employed, 64% work full-time (over 35 hours per week), and 36% work part-time. However, out of all of the mothers in the population, 49% work full-time. The population under study is made up of mothers of junior high school children in Santa Clara County.

Let E = E = size 12{E={}} {} employed, Let F = F = size 12{F={}} {} full-time employment

Exercise 1

  • a. Find the percent of all mothers in the population that NOT employed.
  • b. Find the percent of mothers in the population that are employed part-time.

Solution

  • a. 24%
  • b. 27%

Exercise 2

The type of employment is considered to be what type of data?

Solution

Qualitative

Exercise 3

Find the probability that a randomly selected mother works part-time given that she is employed.

Solution

0.36

Exercise 4

Find the probability that a randomly selected person from the population will be employed OR work full-time.

Solution

0.7636

Exercise 5

Based upon the above information, are being employed AND working part-time:

  • a. mutually exclusive events? Why or why not?
  • b. independent events? Why or why not?

Solution

  • a. No,
  • b. No,

Exercise 6 - Exercise 7 refer to the following: We randomly pick 10 mothers from the above population. We are interested in the number of the mothers that are employed. Let X = X = size 12{X={}} {} number of mothers that are employed.

Exercise 6

State the distribution for X X size 12{X} {} .

Solution

B ( 10 , 0 . 76 ) B ( 10 , 0 . 76 ) size 12{B \( "10",0 "." "76" \) } {}

Exercise 7

Find the probability that at least 6 are employed.

Solution

0.9330

Exercise 8

We expect the Statistics Discussion Board to have, on average, 14 questions posted to it per week. We are interested in the number of questions posted to it per day.

  • a. Define X X size 12{X} {} .
  • b. What are the values that the random variable may take on?
  • c. State the distribution for X X size 12{X} {} .
  • d. Find the probability that from 10 to 14 (inclusive) questions are posted to the Listserv on a randomly picked day.

Solution

  • a. X=X= size 12{X={}} {} the number of questions posted to the Statistics Listserv per day
  • b. x = 0,1,2, . . . x = 0,1,2, . . . size 12{x=0,1,2, "." "." "." } {}
  • c. X ~ P ( 2 ) X ~ P ( 2 ) size 12{X "~" P \( 2 \) } {}
  • d. 0

Exercise 9

A person invests $1000 in stock of a company that hopes to go public in 1 year.

  • The probability that the person will lose all his money after 1 year (i.e. his stock will be worthless) is 35%.
  • The probability that the person’s stock will still have a value of $1000 after 1 year (i.e. no profit and no loss) is 60%.
  • The probability that the person’s stock will increase in value by $10,000 after 1 year (i.e. will be worth $11,000) is 5%.

Find the expected PROFIT after 1 year.

Solution

$150

Exercise 10

Rachel’s piano cost $3000. The average cost for a piano is $4000 with a standard deviation of $2500. Becca’s guitar cost $550. The average cost for a guitar is $500 with a standard deviation of $200. Matt’s drums cost $600. The average cost for drums is $700 with a standard deviation of $100. Whose cost was lowest when compared to his or her own instrument? Justify your answer.

Solution

Matt

Exercise 11

Horizontal boxplot with first whisker extending from 1 to 2, box from 2 to 5,  line at 4, and second whisker extending from 5 to 7.

For each statement below, explain why each is either true or false.

  • a. 25% of the data are at most 5.
  • b. There is the same amount of data from 4 – 5 as there is from 5 – 7.
  • c. There are no data values of 3.
  • d. 50% of the data are 4.

Solution

  • a. False
  • b. True
  • c. False
  • d. False

Exercise 12Exercise 13 refer to the following: 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: Histogram consisting of 5 bars with number of cars, from 0-7 in increments of 1, on the x-axis, and frequency, in increments of 0.1 from 0.15-0.45, on the y-axis. No bars exist for 4, 5, or 7. Bar 0 has a frequency of 0.075, 1 has 0.15, 2 has 0.45, 3 has 0.25, and 6 has 0.075.

Exercise 12

Find the approximate number of responses that were “3.”

Solution

16

Exercise 13

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

Solution

2,2,3 2,2,3 size 12{2,2,3} {}

Exercise 14Exercise 15 refer to the following study done of the Girls soccer team “Snow Leopards”:

Table 1
Hair Style   Hair Color  
  blond brown black
ponytail 3 2 5
plain 2 2 1
Suppose that one girl from the Snow Leopards is randomly selected.

Exercise 14

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

Solution

5 10 = 0 . 5 5 10 = 0 . 5 size 12{ { {5} over {"10"} } =0 "." 5} {}

Exercise 15

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

Solution

7 15 7 15 size 12{ { {7} over {"15"} } } {}

Exercise 16

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

Solution

2 15 2 15 size 12{ { {2} over {"15"} } } {}

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Definition of a lens

Lenses

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What is in a lens?

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Who can create a lens?

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What are tags? tag icon

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Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

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