Question

Suppose the random variable Z follows a standard normal distribution. Calculate each of the following. Round your responses to at least four decimal places. P(-0.32 < Z < 0.63) =

Answer 1

The probability of the random variable Z falling between -0.32 and 0.63 is 0.3595. We calculate this probability by subtracting the cumulative area to the left of -0.32 from the cumulative area to the left of 0.63.

Step-by-step explanation:

In order to determine the probability of the random variable Z falling within the range of -0.32 to 0.63 on the standard normal distribution, one can calculate this probability by subtracting the cumulative area to the left of -0.32 from the cumulative area to the left of 0.63.

Consulting a Z-table, it is found that the area to the left of -0.32 is approximately 0.3745, and the area to the left of 0.63 is about 0.7340.

Consequently, the probability that -0.32 < Z < 0.63 is computed as 0.7340 - 0.3745, resulting in a probability of 0.3595.

This approach leverages the standard normal distribution to ascertain the likelihood of the random variable Z falling within the specified interval, providing a quantitative measure of the probability associated with the given range on the distribution.

Therefore, the probability of -0.32 < Z < 0.63 is 0.7340 - 0.3745 = 0.3595.