## The probability is 51​% that the sample mean will be between what two​ values, symmetrically distributed around the population​ mean? The lo

Question

The probability is 51​% that the sample mean will be between what two​ values, symmetrically distributed around the population​ mean? The lower bound is nothing inches. ​(Round to two decimal places as​ needed.) The upper bound is nothing inches. ​(Round to two decimal places as​ needed.)

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3 weeks 2021-12-29T04:02:39+00:00 1 Answer 0 views 0

## Answers ( )

The lower bound is, and the upper bound is .

Step-by-step explanation:

Let the random variable X follows a normal distribution with mean μ and standard deviation σ.

The the random variable Z, defined as is standardized random variable also known as a standard normal random variable. The random variable  .

The standard normal random variable has a symmetric distribution.

It is provided that .

Determine the upper and lower bound as follows:

Use a standard normal table to determine the value of z.

The value of z such that P (Z ≤ z) = 0.755 is 0.69.

The lower bound is, and the upper bound is .