Use StatCrunch or your calculator to complete each of the following. Be sure to

Question

Use StatCrunch or your calculator to complete each of the following. Be sure to clearly explain your thought process (by showing your StatCrunch output or by-hand calculations) when answering each question, especially if you hope to receive partial credit in the event that your solution is in some way flawed. Please round your answers to no less than 3 decimal places.

1. Four percent of DVD players manufactured by an electronics company are defective. Suppose six DVD players are randomly selected from the production line. Each DVD player is determined to be defective or non-defective.

a. What is the probability that none of the DVD players are defective?

b. What is the probability that all six of the DVD players are defective?

c. What is the probability that at most one of the DVD players is defective?

d. What is the probability that at least two of the DVD players are defective?

2. A basketball player has a history of making 75% of the foul shots taken during games. The player gets two shots at the foul line.

a. What is the probability that he will miss both of the shots?

b. What is the probability that he will make both of the shots?

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
1

a.
P( X = 0 ) = ( 6 0 ) * ( 0.04^0) * ( 1 - 0.04 )^6
= 0.78

b.

P( X < = 6) = P(X=6) + P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0) +
= ( 6 6 ) * 0.04^6 * ( 1- 0.04 ) ^0 + ( 6 5 ) * 0.04^5 * ( 1- 0.04 ) ^1 + ( 6 4 ) * 0.04^4 * ( 1- 0.04 ) ^2 + ( 6 3 ) * 0.04^3 * ( 1- 0.04 ) ^3 + ( 6 2 ) * 0.04^2 * ( 1- 0.04 ) ^4 + ( 6 1 ) * 0.04^1 * ( 1- 0.04 ) ^5 + ( 6 0 ) * 0.04^0 * ( 1- 0.04 ) ^6 +   
= 1

c.
P( X > = 1 ) = 1 - P( X < 1)
P( X < 1) = P(X=0) +   
= ( 6 0 ) * 0.04^0 * ( 1- 0.04 ) ^6 +
= 0.78
P( X > = 1 ) = 1 - P( X < 1) = 0.22

d.
P( X > 2) = 1 - P ( X <=2)
P( X < = 2) = P(X=2) + P(X=1) + P(X=0) +
= ( 6 2 ) * 0.04^2 * ( 1- 0.04 ) ^4 + ( 6 1 ) * 0.04^1 * ( 1- 0.04 ) ^5 + ( 6 0 ) * 0.04^0 * ( 1- 0.04 ) ^6 +   
= 1
P( X > 2) = 1 - P ( X <=2) = 1 -1 = 0

Note: As - per chegg, experts - only - solve - one- question -per -thread. Please -ask -the -remaining -in -different- post

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.