# Normal Probability & t Distribution

See attached file for formulas and amounts.

Question #1 / 5

Let be a standard normal random variable. Use the calculator provided to determine the value of such that .

Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.

Question #2 / 5

Suppose that the heights of adult women in the United States are normally distributed with a mean of inches and a standard deviation of inches. Jennifer is taller than of the population of U.S. women. How tall (in inches) is Jennifer? Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

Question #3 / 5

According to a recent survey, the salaries of assistant professors have a mean of $ and a standard deviation of $ . Assuming that the salaries of assistant professors follow a normal distribution, find the proportion of assistant professors who earn less than $ . Round your answer to at least four decimal places.

Question #4/ 5

Use the calculator provided to solve the following problems.

â?¢ Consider a t distribution with degrees of freedom. Compute . Round your answer to at least three decimal places.

â?¢ Consider a t distribution with degrees of freedom. Find the value of such that . Round your answer to at least three decimal places.

https://brainmass.com/statistics/normal-distribution/normal-probability-distribution-428577

#### Solution Preview

Please see the attachment.

Question #1 / 5

Let be a standard normal random variable. Use the calculator provided to determine the value of such that

.

Carry your intermediate computations to at least four decimal places. Round your answer to at least two decimal places.

Answer

From standard normal table, we have,

P (-1.8599 ≤ Z ≤ 1.8599) = 0.9371

Therefore, c = 1.8599

Question #2 / 5

Suppose that the heights of adult women in the United States are normally distributed with a mean of inches and a standard deviation of inches. Jennifer is taller than of the population of ...

#### Solution Summary

The solution provides step by step method for the calculation of probability using the Z score and t distribution. Formula for the calculation and Interpretations of the results are also included.