Chapter 3.2, Problem 3.31E

(a)

To determine

To calculate the z score from the table at 20^th percentile.

Answer to Problem 3.31E

  ${\text{z value at 20}}^{\text{th}}\text{ percentile = -0}\text{.8416}$

Explanation of Solution

Calculation:

The 20^th percentile means that 20% of the values falls less than that, therefore, it is required to find the value of z below that 20% of the values falls.

P(Z < z) = 0.20 and it is require to find the value of z.

From the standard normal distribution table the value of z is equal to -0.8416.

Therefore, P(z < -0.8416) = 0.20

(b)

To determine

To calculate the z score from the table above that 45% of the data falls.

Answer to Problem 3.31E

Z score above that 45% of the value falls is equal to 0.1257.

Explanation of Solution

Calculation:

The 45% above the z score means that 65% of the values falls less than that. The z score below which 65% of the values falls is 0.1257.