Chapter 6: Q 55 (page 387)

$X ~ N (- 3, 4)$
Find the probability that x is between one and four.

Short Answer

Expert verified

The value of $P (1 < x < 4)$ is $0.1186$ .

Step by step solution

Given Information

Given that,

$X ~ N (- 3, 4)$

Where,

$μ = - 3$ and

$σ = 4$

Explanation

Now, the required probability can be calculated as below:

$P (1 < x < 4) = P (x < 4) - P (x < 1)$

$= P (\frac{x - μ}{σ} < \frac{4 - μ}{σ}) - P (\frac{x - μ}{σ} < \frac{1 - μ}{σ})$

$= P (Z < \frac{4 - (- 3)}{4}) - P (Z < \frac{1 - (- 3)}{4})$

$= P (Z < \frac{7}{4}) - P (Z < \frac{4}{4})$

$= P (Z < 1.75) - P (Z < 1)$

$= 0.9599 - 0.8413 {\begin{cases} From standard \\ normal table \end{cases}}$

$= 0.1186$

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$X ~ N (- 3, 4)$
Find the probability that x is between one and four.

Short Answer

Step by step solution

Given Information

Explanation

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X~N(–3,4)Find the probability that x is between one and four.

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Applied Mathematics

Pure Maths

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

$X ~ N (- 3, 4)$
Find the probability that x is between one and four.