Probability of z > 1.75

B

The area under the curve for z = 1.75 is 0.4599. Therefore, 0.4599*2 = 0.9198. We want z >1.75. So we want (1 - 0.9198)/2 = 0.0401.

To determine the probability that a standard normal random variable (Z) is greater than 1.75, we can refer to the standard normal distribution table or use statistical software.

The standard normal distribution, also known as the Z-distribution, has a mean (μ) of 0 and a standard deviation (σ) of 1. It is a symmetric distribution with the majority of the data clustered around the mean.

Using a standard normal distribution table, we can find the probability associated with a Z-score of 1.75. The table provides the area under the curve to the left of a given Z-score. To find the probability that Z is greater than 1.75, we need to calculate the area to the right of 1.75.

Upon referring to the standard normal distribution table, we find that the area to the left of 1.75 is 0.9599. However, we need the area to the right of 1.75. Since the total area under the curve is 1, we can subtract the area to the left from 1 to obtain the area to the right:

Area to the right of 1.75 = 1 - 0.9599 = 0.0401

Therefore, the probability that Z is greater than 1.75 is 0.0401.

In the provided answers, the correct choice is B. 0.0401.