Chapter 2.2, Problem 52E

(a)

To determine

To find: the valuez from the standard Normal distribution

Answer to Problem 52E

The value of z corresponding to 63^rdpercentile is 0.33.

Explanation of Solution

Given:

The 63^rd percentile.

Calculation:

We are supposed to find the value of z that satisfy the following conditions.

We are supposed to find the value of z corresponding to 0.63

Here 63 percentile indicates that 63% of observations are below the value of 0.63. Using the following standard normal table, we can find the value of z corresponding to 0.63.

  

From the above table, we can see that the value of z corresponding to 0.63 is 0.33.

The following graph illustrates 63^rd percentile along with the corresponding z value as follows:

  

Hence, the value of z corresponding to 63^rd percentile is 0.33.

Conclusion:

Hence, the value of z corresponding to 63^rd percentile is 0.33.

(b)

To determine

To find: the valuez from the standard Normal distribution

Answer to Problem 52E

The value of z such that 75% observations are above zis -0.67.

Explanation of Solution

Given:

75% of all observations are greater than z.

Calculation:

We are supposed to find the value of z such that 75% of all observations are greater than z.

If 75% of observations are above z values, it means that there exists 25% of observations are below z.

  

From the above table, we can observe that the value corresponding to approximated value of 0.25 is -0.67.

  

Hence, the value of z such that 75% observations are above zis -0.67.

Conclusion:

Hence, the value of z such that 75% observations are above zis -0.67.