Suppose X is normally distributed with mean 80 and standard deviation 15.Without using tables,determine the approximate value of P(65

Question

Suppose X is normally distributed with mean 80 and standard deviation 15.Without using tables,determine the approximate value of P(65 < X < 95).
A) 0.997
B) 0.95
C) 0.68
D) 0.50
E) 0.33

Quizplus · Accepted Answer

First, we need to standardize the interval (65, 95) using the formula z = (x - μ) / σ.

For x = 65:

z = (65 - 80) / 15 = -1

For x = 95:

z = (95 - 80) / 15 = 1

So, we want to find P(-1 < Z < 1), where Z is a standard normal variable.

Using the empirical rule (or 68-95-99.7 rule), we know that approximately 68% of the observations fall within one standard deviation of the mean. Since the normal distribution is symmetric, this means that

P(-1 < Z < 1) ≈ 0.68

Therefore, the answer is C.

Suppose X Is Normally Distributed with Mean 80 and Standard