Chapter 2, Problem 8CRE

(a)

To determine

To find: the number $z$ at the ${80}^{\text{th}}$ percentile

Answer to Problem 8CRE

The value of $z$ corresponding to ${80}^{\text{th }}$ percentile is 0.84

Explanation of Solution

Calculation:

We are supposed to find the value of $z$ corresponding to ${80}^{\text{th }}$ percentile.

Consider the following standard normal table.

  

From the above table, we can see that the value of $z$ corresponding to approximated value of

0.80 is 0.84

Hence, the value of $z$ corresponding to ${80}^{\text{th }}$ percentile is 0.84

Conclusion:

Hence, the value of $z$ corresponding to ${80}^{\text{th }}$ percentile is 0.84

(b)

To determine

To find: the number $z$

Answer to Problem 8CRE

The value of $z$ corresponding to approximated value is 0.39

Explanation of Solution

Given:

  $35\%$ of all observations from a standard Normal distribution are greater than $z$ .

Calculation:

We are supposed to find the value of $z$ such that $35\%$ of all observations from Standard Normal distribution are greater than $z$ . As $35\%$ of observations are greater than $z$ , we can say that $65\%$ of observations are less than $z$

  

From the above table, we can see that the value of $z$ corresponding to approximated value of

0.65 is 0.39

Hence, the number $z$ such that $35\%$ of all observations from Standard Normal distribution aregreater than $z$ is 0.39

Conclusion:

Hence, the value of $z$ corresponding to approximated value is 0.39