Question

For a standard normal distribution, suppose the following is true:

P(z < c) = 0.0166

Find c.

Answer 1

Using a standard normal distribution table, we can find the z-score corresponding to a probability of 0.0166:

z = -2.07

Therefore, c = -2.07.

Explanation:

Answer 2

From the given information, we know that the area to the left of c under the standard normal distribution curve is 0.0166.

Using a standard normal distribution table or calculator, we can find the corresponding z-score for this area.

A z-score represents the number of standard deviations away from the mean. For a standard normal distribution, the mean is 0 and the standard deviation is 1.

Looking up the area of 0.0166 in the z-table, we find that the corresponding z-score is approximately -2.06.

Therefore, we have:

P(z < c) = 0.0166

P(z < -2.06) = 0.0166

So, c = -2.06.