Question

Use the following information to answer the next four exercises:

$X~N(54,8)$

Find the probability that$x>56.$

Short answer

The probability that$x>56$is$0.4013$

Step-by-step solution

Given Information 

Given in the question that,

$X~N(54,8)$

We have to find the probability that$x>56$

Explanation 

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

$p(X>56)=1-p(X\le 56)$

$=1-p\left(Z\le \frac{X-\mu }{\sigma }\right)$

$=1-p\left(Z\le \frac{56-54}{8}\right)$

$=1-p(Z\le 0.25)$

Apply the probability rule 

Apply the probability rule to compute the value of $P(Z\le 0.25)$

$P(Z\le a)=P(Z\le 0)+P(0\le Z\le a)$

$a=0.25$

$=P(Z\le 0)+P(0\le Z\le 0.25)$

$P(Z\le 0)=0.5$

Cumulative probability of $P(0\le Z\le 0.25)$:

$=0.5+0.0987$

$=0.5987$

Place the value 

Place the value of $P(Z\le 2.5)$in the above formula

$p(X>56)=1-p(Z\le 0.25)$

$=1-0.5987$

$=0.4013$