Question

Let x be a continuous random variable that follows a normal distribution with a mean of 200 and a standard deviation of 24. Find the value of x so that the area under the normal curve to the left of approximately 0.9924

a) 240
b) 252
c) 264
d) 276

Answer 1

To find the value of x so that the area under the normal curve to the left is approximately 0.9924, we can use the z-score formula. The value of x is approximately 252.

Step-by-step explanation:

To find the value of x so that the area under the normal curve to the left is approximately 0.9924, we need to find the z-score that corresponds to this area. The z-score is a measure of how many standard deviations a value is from the mean in a normal distribution.

Using a standard normal distribution table or a calculator, we find that the z-score corresponding to an area of 0.9924 to the left is approximately 2.33. Then, we can use the z-score formula to find the value of x:

x = z * σ + μ

Substituting the given values, we get:

x = 2.33 * 24 + 200 = 252

Therefore, the value of x is approximately 252.