Assume that X is normally distributed with a mean of 5 and

Chapter 4, Problem 70E

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QUESTION:

Assume that X is normally distributed with a mean of 5 and a standard deviation of 4. Determine the value for x that solves each of the following:

(a) \(P(X>x)=0.5\)

(b) \(P(X>x)=0.95\)

(c) \(P(x<X<9)=0.2\)

(d) \(P(3<X<x)=0.95\)

(e) \(P(-x<X-5<x)=0.99\)

Questions & Answers

QUESTION:

Assume that X is normally distributed with a mean of 5 and a standard deviation of 4. Determine the value for x that solves each of the following:

(a) \(P(X>x)=0.5\)

(b) \(P(X>x)=0.95\)

(c) \(P(x<X<9)=0.2\)

(d) \(P(3<X<x)=0.95\)

(e) \(P(-x<X-5<x)=0.99\)

ANSWER:

Solution:

Step 1 of 6:

Let X is a normally distributed with a mean of 5 and a standard deviation of 4.

We have to find value for x that satisfying the following probabilities.

  1. P(X>x) = 0.5
  2. P(X>x) = 0.95
  3. P(x<X<9)= 0.2
  4.  P(3<X<x) = 0.95
  5. P(-x<X-5<x) = 0.99


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