If the random variable x is normally distributed with a mean of 88 and a standard deviation of 12, then P(X 96) is:
A) 0.2486
B) 0.2514
C) 0.1243
D) 0.4972
E) 0.3398

Question

If the random variable x is normally distributed with a mean of 88 and a standard deviation of 12, then P(X  96) is:
A) 0.2486 
B) 0.2514 
C) 0.1243 
D) 0.4972 
E) 0.3398

Quizplus · Accepted Answer

To solve this problem, we need to standardize the random variable x using the formula:

z = (x - μ) / σ

where μ is the mean and σ is the standard deviation.

So, for P(11 < x < 96), we get:

z1 = (11 - 88) / 12 = -6.42
z2 = (96 - 88) / 12 = 0.67

Now, we need to find the area under the standard normal curve between z1 and z2. Using a standard normal table or a calculator, we get:

P(-6.42 < z < 0.67) = 0.2514

Therefore, the answer is B.

If the Random Variable X Is Normally Distributed with a Mean