Suggested languages for you:

Americas

Europe

Q. 50

Expert-verified
Found in: Page 387

### Introductory Statistics

Book edition OER 2018
Author(s) Barbara Illowsky, Susan Dean
Pages 902 pages
ISBN 9781938168208

# Use the following information to answer the next four exercises:$X~N\left(54,8\right)$Find the probability that $x>56.$

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

See the step by step solution

## Step 1: Given Information

Given in the question that,

$X~N\left(54,8\right)$

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

## Step 2: Explanation

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

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

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

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

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

## Step 3: Apply the probability rule

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

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

$a=0.25$

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

$P\left(Z\le 0\right)=0.5$

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

$=0.5+0.0987$

$=0.5987$

## Step 4: Place the value

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

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

$=1-0.5987$

$=0.4013$