Respuesta :
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,
[tex]P(Z<z) = 0.36[/tex]
This value will be calculated with the help of a standard normal table.
From standard normal table we have,
[tex]P(z\leq -0.358) = 0.36[/tex]
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.
[tex]P(Z>z) = 0.36[/tex]
This value will be calculated with the help of a standard normal table.
[tex]= 1 -P( Z > z)=1 - 0.36 = 0.64[/tex]
[tex]P( z \leq z)=0.64[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z \leq 0.358) = 0.64[/tex]
Thus, 36% of all observations from a standard normal distribution are greater than z equal to 0.358
