Question

(a) Find z such that the proportion of observations that are less than z in a standard normal distribution is 0.36. (Enter your answer rounded to two decimal places.)
(b) Find z such that 36% of all observations from a standard normal distribution are greater than z. (Enter your answer rounded to two decimal places.)

Answer 1

Answer:

a) z = -0.358

b) z = 0.358              

Step-by-step explanation:

We are given a standard normal distribution.

a) We have to find the value of z such that the proportion of observations that are less than z in a standard normal distribution is 0.36.

That is,

$P(Z$

This value will be calculated with the help of a standard normal table.

From standard normal table we have,

$P(z\leq -0.358) = 0.36$

Thus, for z equal to -0.358 the proportion of observations that are less than z in a standard normal distribution is 0.36

b) We have to find the value of z such that 36% of all observations from a standard normal distribution are greater than z.

$P(Z>z) = 0.36$

This value will be calculated with the help of a standard normal table.

$= 1 -P( Z > z)=1 - 0.36 = 0.64$  

$P( z \leq z)=0.64$  

Calculation the value from standard normal z table, we have,

$P(z \leq 0.358) = 0.64$

Thus, 36% of all observations from a standard normal distribution are greater than z equal to 0.358