Q. 6.8 - Elementary Statistics

Question

Obtain the following $z-$scores

a. $z_{0.20}$

b. $z_{0.06}$

Step-by-Step Solution

Answer

(a) The $z-$score under the usual normal curve with the area $0.20$ to its right is around $0.84$.

(b) The $z-$score with a right-hand area of $0.06$ under the usual normal curve is around $0.1555$. 

Part (a) Step 1: Given information

The given area is $0.20$.

Part (a) Step 2: Explanation

The area is $0.20$

The $z-$score for which the area under the standard normal curve to its right is $0.20$ will be identical to the z-score for which the area under the standard normal curve to its left is $1-0.20=0.80$.

Begin by looking for the $0.80$ area in the table's body. It is not included in the table, and the closest value is $0.7995$. The associated $z-$score is $0.84$.

As a result, the $z-$score under the usual normal curve with the area $0.20$ to its right is around $0.84$, which may be depicted as

Below is a section of the standard normal table that is relevant:

Part (b) Step 1: Given information

The given area is $0.06.$

Part (b) Step 2: Explanation

The area is $0.06$

The $z-$score for which the area under the standard normal curve to its right is will be identical to the z-score for which the area under the standard normal curve to its right is $0.06$.

to the left of $1-0.06=0.94$

Begin by looking in the table's body for the area $0.94$. It is not in the database, and the closest values are $0.9394$ and $0.9406$ in the table. $1.55$ is the average $z-$score of $1.55$ and $1.56$.

As a result, the $z-$score with a right-hand area of $0.06$ under the usual normal curve is around $1.555$, which may be depicted

Below is a section of the standard normal table that is relevant: