Question

For some postive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770. The value of Z is

Answer 1

1.16

Explanation:

Given that;

For some positive value of Z, the probability that a standardized normal variable is between 0 and Z is 0.3770.

This implies that:

P(0<Z<z) = 0.3770

P(Z < z)-P(Z < 0) = 0.3770

P(Z < z) = 0.3770 + P(Z < 0)

From the standard normal tables , P(Z < 0) =0.5

P(Z < z) = 0.3770 + 0.5

P(Z < z) = 0.877

SO to determine the value of z for which it is equal to 0.877, we look at the

table of standard normal distribution and locate the probability value of 0.8770. we advance to the left until the first column is reached, we see that the value was 1.1. similarly, we did the same in the upward direction until the top row is reached, the value was 0.06. The intersection of the row and column values gives the area to the two tail of z. (i.e 1.1 + 0.06 =1.16)

therefore, P(Z ≤ 1.16 ) = 0.877