Question

What percent of a standard normal distribution N(? = 0, ? = 1) is found in each region?

(A) Z > -1.13
(B) Z < 0.18
(C) Z > 8
(D) |Z| < 0.5

Answer 1

To find the percent of a standard normal distribution in each region, we use Z-scores and the cumulative distribution function (CDF). For each given region, we find the probability using a Z-table or calculator. For Z > -1.13, the probability is approximately 87.08%. For Z < 0.18, the probability is approximately 57.26%. For Z > 8, the probability is negligible, and for |Z| < 0.5, the probability is approximately 38.29%.

Step-by-step explanation:

To find the percent of a standard normal distribution in each region, we need to use the Z-scores and the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives us the probability that a random variable from the standard normal distribution is less than or equal to a specific Z-score.

A) For Z > -1.13, we need to find the probability that the Z-score is greater than -1.13. Using a Z-table or calculator, we find the probability to be approximately 0.8708, or 87.08%.

B) For Z < 0.18, we need to find the probability that the Z-score is less than 0.18. Using a Z-table or calculator, we find the probability to be approximately 0.5726, or 57.26%.

C) For Z > 8, we need to find the probability that the Z-score is greater than 8. However, the standard normal distribution is defined within a range of -3 to 3, so the probability is essentially negligible. We can approximate it as 0.

D) For |Z| < 0.5, we need to find the probability that the absolute value of the Z-score is less than 0.5. Using a Z-table or calculator, we find the probability to be approximately 0.3829, or 38.29%.