CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 7. Sampling Distributions and Estimations

variable,X, defined as the number of students that take the bus to school. (Hint: Begin by listing all of the

possible outcomes).

2. The Safe Grad Committee at the high school is selling tickets on a Christmas Basket filled with gifts and
   gift cards. The prize is valued at $1200 and the committee has decided to sell only 500 tickets. What is the
   expected value of a ticket? If the students decide to sell tickets on three monetary prizes – one of $1500 dollars
   and two of $500 each, what is the expected value of the ticket now?


3. A recent law has been passed banning the use of hand-held cell phones while driving. A survey has revealed
   that 76% of drivers now refrain from using the cell phone while driving. Three drivers were randomly selected
   and a probability distribution table was constructed to record the outcomes. Let N represent those drives who
   never use the cell phone while driving andSrepresent those who seldom use the cell phone. Calculate the
   expected value and the variance using technology.

Review Answers

1. Outcomes and their probabilities are:

P (none take the bus)= ( 0. 3 )( 0. 3 )( 0. 3 ) = 0. 027

p (only the first student takes the bus)= ( 0. 7 )( 0. 3 )( 0. 3 ) = 0. 063

P (only the second student takes the bus)= ( 0. 3 )( 0. 7 )( 0. 3 ) = 0. 063

P (only the third student takes the bus)= ( 0. 3 )( 0. 3 )( 0. 7 ) = 0. 063

P (the first and second students take the bus)= ( 0. 7 )( 0. 7 )( 0. 3 ) = 0. 147

P (the second and third students take the bus)= ( 0. 3 )( 0. 7 )( 0. 7 ) = 0. 147

P (the first and third students take the bus)= ( 0. 7 )( 0. 3 )( 0. 7 ) = 0. 147

P (all three students take the bus)= ( 0. 7 )( 0. 7 )( 0. 7 ) = 0. 343

TABLE7.22:

Number of Students Who Ride the Bus,x Probability,p

0 0. 027

1 ( 3 )( 0. 063 ) = 0. 189

2 ( 3 )( 0. 147 ) = 0. 441

3 0. 343

2.

μx= 1200 ·

1

500

+ 0 ·

499

500

=$2. 40 The expected value of the ticket

for the gift basket is $2. 40.

μx= 1500 ·

1

500

+ 500 ·

2

500

+·

497

500

=$5. 00 The expected value of the ticket

for three prize draws is $5. 00

TABLE7.23:

Outcome Probability

NNN ( 0. 76 )( 0. 76 )( 0. 76 ) =. 438976

NNS ( 0. 76 )( 0. 76 )( 0. 24 ) =. 138624