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Confidence Intervals: Review

Module by: Dr. Barbara Illowsky, Susan Dean

The next three problems refer to the following situation: Suppose that a sample of 15 randomly chosen people were put on a special weight loss diet. The amount of weight lost, in pounds, follows an unknown distribution with mean equal to 12 pounds and standard deviation equal to 3 pounds.

Exercise 1

To find the probability that the average of the 15 people lose no more than 14 pounds, the random variable should be:

  • A. The number of people who lost weight on the special weight loss diet
  • B. The number of people who were on the diet
  • C. The average amount of weight lost by 15 people on the special weight loss diet
  • D. The total amount of weight lost by 15 people on the special weight loss diet

Solution 1

C

Exercise 2

Find the probability asked for in the previous problem.

Solution 2

0.9951

Exercise 3

Find the 90th percentile for the average amount of weight lost by 15 people.

Solution 3

12.99

The next three questions refer to the following situation: The time of occurrence of the first accident during rush-hour traffic at a major intersection is uniformly distributed between the three hour interval 4 p.m. to 7 p.m. Let X X size 12{X} {} = the amount of time (hours) it takes for the first accident to occur.

  • So, if an accident occurs at 4 p.m., the amount of time, in hours, it took for the accident to occur is _______.
  • μ = μ = size 12{μ} {} _______
  • σ 2 = σ 2 = size 12{σ rSup { size 8{2} } } {} _______

Exercise 4

What is the probability that the time of occurrence is within the first half-hour or the last hour of the period from 4 to 7 p.m.?

  • A. Cannot be determined from the information given
  • B. 1 6 1 6 size 12{ { { size 8{1} } over { size 8{6} } } } {}
  • C. 1 2 1 2 size 12{ { { size 8{1} } over { size 8{2} } } } {}
  • D. 1 3 1 3 size 12{ { { size 8{1} } over { size 8{3} } } } {}

Solution 4

C

Exercise 5

The 20th percentile occurs after how many hours?

  • A. 0.20
  • B. 0.60
  • C. 0.50
  • D. 1

Solution 5

B

Exercise 6

Assume Ramon has kept track of the times for the first accidents to occur for 40 different days. Let C C size 12{C} {} = the total cumulative time. Then C C size 12{C} {} follows which distribution?

  • A. U ( 0,3 ) U ( 0,3 ) size 12{U \( 0,3 \) } {}
  • B. Exp ( 1 3 ) Exp ( 1 3 ) size 12{ ital "Exp" \( { { size 8{1} } over { size 8{3} } } \) } {}
  • C. N ( 60 , 30 ) N ( 60 , 30 ) size 12{N \( "60","30" \) } {}
  • D. N ( 1 . 5,0 . 01875 ) N ( 1 . 5,0 . 01875 ) size 12{N \( 1 "." 5,0 "." "01875" \) } {}

Solution 6

C

Exercise 7

Using the information in question #6, find the probability that the total time for all first accidents to occur is more than 43 hours.

Solution 7

0.9990

The next two questions refer to the following situation: The length of time a parent must wait for his children to clean their rooms is uniformly distributed in the time interval from 1 to 15 days.

Exercise 8

How long must a parent expect to wait for his children to clean their rooms?

  • A. 8 days
  • B. 3 days
  • C. 14 days
  • D. 6 days

Solution 8

A

Exercise 9

What is the probability that a parent will wait more than 6 days given that the parent has already waited more than 3 days?

  • A. 0.5174
  • B. 0.0174
  • C. 0.7500
  • D. 0.2143

Solution 9

C

The next five problems refer to the following study: Twenty percent of the students at a local community college live in within five miles of the campus. Thirty percent of the students at the same community college receive some kind of financial aid. Of those who live within five miles of the campus, 75% receive some kind of financial aid.

Exercise 10

Find the probability that a randomly chosen student at the local community college does not live within five miles of the campus.

  • A. 80%
  • B. 20%
  • C. 30%
  • D. Cannot be determined

Solution 10

A

Exercise 11

Find the probability that a randomly chosen student at the local community college lives within five miles of the campus or receives some kind of financial aid.

  • A. 50%
  • B. 35%
  • C. 27.5%
  • D. 75%

Solution 11

B

Exercise 12

Based upon the above information, are living in student housing within five miles of the campus and receiving some kind of financial aid mutually exclusive?

  • A. Yes
  • B. No
  • C. Cannot be determined

Solution 12

B

Exercise 13

The interest rate charged on the financial aid is _______ data.

  • A. quantitative discrete
  • B. quantitative continuous
  • C. qualitative discrete
  • D. qualitative

Solution 13

B

Exercise 14

What follows is information about the students who receive financial aid at the local community college.

  • 1st quartile = $250
  • 2nd quartile = $700
  • 3rd quartile = $1200

(These amounts are for the school year.) If a sample of 200 students is taken, how many are expected to receive $250 or more?

  • A. 50
  • B. 250
  • C. 150
  • D. Cannot be determined

Solution 14

  • C. 150

The next two problems refer to the following information: P ( A ) = 0 . 2 P ( A ) = 0 . 2 size 12{P \( A \) =0 "." 2} {} , P ( B ) = 0 . 3 P ( B ) = 0 . 3 size 12{P \( B \) =0 "." 3} {} , A A size 12{A} {} and B B size 12{B} {} are independent events.

Exercise 15

P(AANDB)=P(AANDB)= size 12{P \( A} {}

  • A. 0.5
  • B. 0.6
  • C. 0
  • D. 0.06

Solution 15

D

Exercise 16

P(AORB)=P(AORB)= size 12{P \( A} {}

  • A. 0.56
  • B. 0.5
  • C. 0.44
  • D. 1

Solution 16

C

Exercise 17

If H H size 12{H} {} and D D size 12{D} {} are mutually exclusive events, {} P ( H ) = 0 . 25 P ( H ) = 0 . 25 size 12{P \( H \) =0 "." "25"} {} , P ( D ) = 0 . 15 P ( D ) = 0 . 15 size 12{P \( D \) =0 "." "15"} {} , then P(H| D )P(H| D ) size 12{P \( H} {}

  • A. 1
  • B. 0
  • C. 0.40
  • D. 0.0375

Solution 17

B

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