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Chapter 6: Q. 80 (page 404)

80. More lefties Refer to Exercise 72.

(a) Find the probability that exactly 3students in the sample are left-handed. Show your work.
(b) Would you be surprised if the random sample contained 4or more left-handed students? Compute P(W≥4) and use this result to support your
answer.

Short Answer

Expert verified

(a) The probability is P(X=3)=12.85%

(b) The probability is P(X≥4)≈5.56%and not surprised by 4 or more left-handed students.

Step by step solution

01

Part (a) Step 1: Given information 

The probability that exactly 3students in the sample are left-handed.

02

Part (a) Step 2: Explanation 

Given: n=15, andp=0.10

The Binomial Probability:

P(X=k)=nk×pk×(1-p)n-k

Then for k=3,

P(X=3)=153×(0.10)3×(0.90)15-3

localid="1650028682048" ≈0.1285=12.85%.

03

Part (b) Step 1: Given information 

The random sample contained 4 or more left-handed students. And compute for the value P(W≥4).

04

Part (b) Step 2: Explanation 

Given: n=20and p=0.85

The Binomial Probability:

P(X=k)=nk×pk×(1-p)n-k
P(X≥4)=P(X=4)+P(X=5)+…+P(X=15)≈0.0556≈5.56%

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