Let the random variable Z follow a standard normal distribution.Find the value k,such that P(-0.62

Question

Let the random variable Z follow a standard normal distribution.Find the value k,such that P(-0.62 < Z < k)= 0.43.
A)0.20
B)0.52
C)0.12
D)0.56

Quizplus · Accepted Answer

Since Z follows a standard normal distribution, we know that P(-∞ < Z < ∞) = 1. Let's call the probability in question as P1, then we can write:
P1 = P(-0.62 < Z < k) = 0.43
We know that the standard normal distribution is symmetric around 0, so we can find the value of k by finding the difference between the area to the left of k and the area to the left of -0.62. We can use a standard normal distribution table or calculator to find these areas, which are approximately 0.267 and 0.2676, respectively. The difference between these areas is approximately 0.0006. Since we want the total area between -0.62 and k to be 0.43, we need to find the area to the right of k, which is approximately 0.43 + 0.0006 = 0.4306. We can use a standard normal distribution table or calculator again to find the value of k that corresponds to this area, which is approximately 0.52. Hence, the answer is B.

Let the Random Variable Z Follow a Standard Normal Distribution