Question

9. Using our text’s z-table, find the proportion under the curve that lies between each of the following: a. The mean & z = 1.96 b. The mean & z = -0.83 c. z = -1.5 & z = 1.5 d. z = -0.3 & z = -0.1 e. z = -1.65 & z = 1.45

Answer 1

Solution :

Using standard normal table,

(a)

P(0 < z < 1.96) = P(z < 1.6) - P(z < 0) = 0.975 - 0.5 = 0.475

Proportion = 0.475

(b)

P( -0.83 < z < 0) = P(z < 0) - P(z < -0.83) = 0.5 - 0.2033 = 0.2967

(c)

P(-1.5 < z < 1.5) = P(z < 1.5) - P(z < -1.5) = 0.9332 - 0.0668 = 0.8664

Proportion = 0.8664

(d)

P(-0.3 < z < -0.1) = P(z < -0.1) - P(z < -0.3) = 0.4602 - 0.3821 = 0.0781

(e)

P(-1.65 < z < 1.45) = P(z < 1.45) - P(z < -1.65) = 0.9265 - 0.0495 = 0.877

Proportion = 0.877

(e)