Chapter 6: Q. 50 (page 387)

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

Short Answer

Expert verified

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:

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

$= 1 - p (Z \leq \frac{X - μ}{σ})$

$= 1 - p (Z \leq \frac{56 - 54}{8})$

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

Apply the probability rule

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

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

$a = 0.25$

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

$P (Z \leq 0) = 0.5$

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

$= 0.5 + 0.0987$

$= 0.5987$

Place the value

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

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

$= 1 - 0.5987$

$= 0.4013$

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

Short Answer

Step by step solution

Given Information

Explanation

Apply the probability rule

Place the value

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Use the following information to answer the next four exercises:X~N(54,8)Find the probability thatx>56.

Short Answer

Step by step solution

Given Information

Explanation

Apply the probability rule

Place the value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Decision Maths

Applied Mathematics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

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