THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of 17.1 and a standard deviation of 3.2.
-What is P(15

Question

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of 17.1 and a standard deviation of 3.2.
-What is P(15 < X < 20)?
A)0.5581
B)0.1814
C)0.5640
D)0.2546

Quizplus · Accepted Answer

Using the standard normal distribution table, we first convert the values of X to z-scores:
z(15) = (15-17.1)/3.2 = -0.65625 
z(20) = (20-17.1)/3.2 = 0.90625
Then, we look up the area under the standard normal curve between these two z-scores:
P(-0.65625 < Z < 0.90625) = 0.5640
Therefore, the answer is choice C: 0.5640.