Understandable Statistics: Concepts and Methods
Understandable Statistics: Concepts and Methods
12th Edition
ISBN: 9781337119917
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Chapter 4, Problem 12CRP

a.

To determine

Find the values of P(N), P(M) and P(S).

a.

Expert Solution
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Answer to Problem 12CRP

The value of P(N) is 0.470.

The value of P(M) is 0.390.

The value of P(S) is 0.140.

Explanation of Solution

It is given that the events W, A, S, M and N are defined as follows:

W=washing oil off within 5 minute, A=washing oil off after 5 minute

S=Strong reaction, N=no reaction, M=mild reaction

There are 470 people under the event with no reaction and the total number people who participated in the study are 1000.

The value of P(N) is as follows:

P(S)=4701,000=0.470

Thus, the value of P(N) is 0.470.

The value of P(M) is as follows:

P(M)=3901,000=0.390

Thus, the value of P(M) is 0.390.

The value of P(S) is computed as follows:

P(S)=1401,000=0.140

Therefore, the value of P(S) is 0.140.

b.

To determine

Find the values of P(N/W) and P(S/W).

b.

Expert Solution
Check Mark

Answer to Problem 12CRP

The value of P(N/W) is 0.84.

The value of P(S/W) is 0.04.

Explanation of Solution

The value of P(N/W) is computed as follows:

P(N/W)=P(N and W)P(W)=420500  {from the given table}=0.84

Thus, the value of P(N/W) is 0.84.

The value of P(S/W) is as follows:

P(S/W)=P(S and W)P(W)=20500  {from the given table}=0.04

Therefore, the value of P(S/W) is 0.04.

c.

To determine

Find the values of P(N/A) and P(S/A).

c.

Expert Solution
Check Mark

Answer to Problem 12CRP

The value of P(N/A) is 0.100.

The value of P(S/A) is 0.240.

Explanation of Solution

The value of P(N/A) is as follows:

P(N/A)=P(N and A)P(A)=50500   {from the given table}=0.100

Thus, the value of P(N/A) is 0.100.

The value of P(S/A) is computed as follows:

P(S/A)=P(S and A)P(A)=120500=0.240

Therefore, the value of P(S/A) is 0.240.

d.

To determine

Find the values of P(N and W) and P(M and W).

d.

Expert Solution
Check Mark

Answer to Problem 12CRP

The value of P(N and W) is 0.420.

The value of P(M and W) is 0.060.

Explanation of Solution

The value of P(N and W) is as follows:

P(N and W)=P(W)×P(N/W)=5001,000×420500=4201,000=0.420

Thus, the value of P(N and W) is 0.420.

The value of P(M and W) is as follows:

P(M and W)=P(W)×P(M/W)=5001,000×60500=601,000=0.060

Thus, the value of P(M and W) is 0.060.

e.

To determine

Compute the value of P(or M).

Explain whether the events N=no reaction and A=mild reaction are mutually exclusive.

e.

Expert Solution
Check Mark

Answer to Problem 12CRP

The value of P(or M) is 0.860.

Explanation of Solution

Yes, the events N=no reaction and A=mild reaction are mutually exclusive, because these events cannot occur at the same time.

The value of P(or M) is as follows:

P(or M)=P(N)+P(M)=0.470+0.390  {from Part(a)}=0.860

Thus, the value of P(or M) is 0.860.

f.

To determine

Explain whether the events N=no reaction and W=washing oil off within 5 minute are independent or not.

f.

Expert Solution
Check Mark

Answer to Problem 12CRP

The events N and W are not independent.

Explanation of Solution

The events N and W are said to be independent if P(N and W)=P(N)×P(W).

From Part (a), the value of P(N) is 0.470.

From Part (d), the value of P(W) is 0.500, and the value of P(N and W) is 0.420.

The R.H.S P(N)×P(W) of the independent condition is as follows:   

P(N)×P(W)=0.470×0.500=0.235P(N and W)L.H.S

Since the condition P(N and W)=P(N)×P(W) is not satisfied. Therefore, the events N and W arenot independent.

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Chapter 4 Solutions

Understandable Statistics: Concepts and Methods

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