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.)

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 .