Let the random variable Z follow a standard normal distribution.

a. The probability is 0.70 that Z is less than what number?

b. The probability is 0.25 that Z is less than what number?

c. The probability is 0.2 that Z is greater than what number?

d. The probability is 0.6 that Z is greater than what number?

(a) z = 0.53

(b) z -0.67

(c) z = -0.84

(d) z = 0.26

Explanation:

A standard normal distribution has mean 0 and standard deviation 1.

(a)

Compute the value of z for P (Z < z) = 0.70 as follows:

Consider the standard normal table for the value of z.

The value of z is 0.53.

(b)

Compute the value of z for P (Z < z) = 0.25 as follows:

Consider the standard normal table for the value of z.

The value of z is -0.67.

(c)

Compute the value of z for P (Z > z) = 0.20 as follows:

P (Z > z) = 0.20

1 - P (Z < z) = 0.20

P (Z < z) = 0.80

Consider the standard normal table for the value of z.

The value of z is -0.84.

(d)

Compute the value of z for P (Z > z) = 0.60 as follows:

P (Z > z) = 0.60

1 - P (Z < z) = 0.60

P (Z < z) = 0.40

Consider the standard normal table for the value of z.

The value of z is 0.26.

d. all of the above are true.