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Chapter 6: Q. 50 (page 387)

Use the following information to answer the next four exercises:

X~N(54,8)

Find the probability thatx>56.

Short Answer

Expert verified

The probability thatx>56is0.4013

Step by step solution

01

Given Information 

Given in the question that,

X~N(54,8)

We have to find the probability thatx>56

02

Explanation 

According to the given information, we can compute the probability as follow:

p(X>56)=1鈭�p(X鈮�56)

=1鈭�pZ鈮�X鈭�渭蟽

=1鈭�pZ鈮�56鈭�548

=1鈭�p(Z鈮�0.25)

03

Apply the probability rule 

Apply the probability rule to compute the value of P(Z鈮�0.25)

P(Z鈮�a)=P(Z鈮�0)+P(0鈮�Z鈮�a)

a=0.25

=P(Z鈮�0)+P(0鈮�Z鈮�0.25)

P(Z鈮�0)=0.5

Cumulative probability of P(0鈮�Z鈮�0.25):

=0.5+0.0987

=0.5987

04

Place the value 

Place the value of P(Z鈮�2.5)in the above formula

p(X>56)=1鈭�p(Z鈮�0.25)

=1鈭�0.5987

=0.4013

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