Question

Suppose Z follows the standard normal distribution. determine the value of c so that the following is true.P= (-c ≤ Z ≤ c) =0.9464Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places. AND AGAIN DONT FORGOT TO Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.

Answer 1

c = 1.93

Explanation

Graphically, the probability: P(-c ≤ Z ≤ c) is represented by the area under the curve of z-scores, that is,

Given that the curve is symmetrical, then the area on the right is half the total area.

The probability: P(Z ≤ c) = 0.4732 is found in the following table:

The area of 0.4732 corresponds to P(z < 1.93), then c = 1.93