Question

Find the area of the shaded region. The graph to the right depicts IQ scores of​ adults, and those scores 75 are normally distributed with a mean of 100 and a standard deviation of 15.

Answer 1

the area of the shaded region is 0.9525 (rounded to four decimal places).

Explanation:

Since IQ scores above 75 are shaded, we need to find the area to the right of 75 on the normal distribution curve with mean 100 and standard deviation 15.

Using a standard normal table or calculator, we can find the z-score corresponding to 75 as follows:

z-score = (75 - 100) / 15 = -1.67

The area to the right of this z-score is the probability that an IQ score is above 75, which is the shaded area in the graph.

Using a standard normal table or calculator, we find that the area to the right of a z-score of -1.67 is 0.9525 (rounded to four decimal places).

Therefore, the area of the shaded region is 0.9525 (rounded to four decimal places).