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# Finding Probabilities in normal distribution

Problem:1 Suppose that x is normally distributed random variable with µ = 11 and variance = 4. Find each of the following:
a)P(10<x <12)
b)P(x > 13.24)
c)P(x < x0) 0.75 find Xo

Problem:2.Consider the following hypothesis test.

Ho: µ >; 10
Ha: µ < 10

A sample with n = 50 provides a sample mean of 9.46 and sample standard deviation of 2. At alpha = 0.05, what is the critical value for z or t? What is the rejection rule?

#### Solution Preview

Note : Please see the attached file. Work done in equation editor may be missing or may not properly print here.

Suppose that x is normally distributed random variable with µ = 11 and &#963;2 = 4. Find each of the following:

a) P(10&#8804; x &#8804;12)

.
Let us find Z for X=10, and X=12. Z is given by

For X=10,

Negative sign implies that value of X lies in left side of mean.

From the tables we get Corresponding value of Probability = 0.1915

For X=12,
Positive sign implies that value of X lies in right side of mean.

From the tables we get Corresponding value of Probability = 0.1915

For ...

#### Solution Summary

Solution explains the steps in finding probability for different values of X. X is normally distributed.
Second problem is about hypothesis testing for normal distribution. Critical Value of Z and rejection rule have been worked out.

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