Question

You may need to use the appropriate appendix table to answer this question.

Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)

(a) The area to the left of z is 0.9750.

(b) The area between 0 and z is 0.4750.

(c) The area to the left of z is 0.7486.

(d) The area to the right of z is 0.1210.

(e) The area to the left of z is 0.7088.

(f) The area to the right of z is 0.2912.

Answer 1

Solution :

Using standard normal table,

(a)

P(Z < z) = 0.9750

P(Z < 1.96) = 0.9750

z = 1.96

(b)

P(0 < Z < z) = 0.4750

P(Z < z) - P(Z < 0) = 0.4750

P(Z < z) - 0.5 = 0.4750

P(Z < z) = 0.5 + 0.4750 = 0.9750

P(Z < 1.96) = 0.9750

z = 1.96

(c)

P(Z < 0.67) = 0.7486

z = 0.67

(d)

P(Z > z) = 0.1210

1 - P(Z < z) = 0.1210

P(Z < z) = 1 - 0.1210 = 0.879

P(Z < 1.17) = 0.879

z = 1.17

(e)

P(Z < 0.55) = 0.7088

z = 0.55

(f)

P(Z > z) = 0.2912

1 - P(Z < z ) = 0.2912

P(Z < z) = 1 - 0.2912 = 0.7088

P(Z < 0.55) = 0.7088

z = 0.55