Question

Assume a normal distribution with mean = 100 and standard deviation = 10. What is the probability that X is greater than 80?

A) 0.0228
B) 0.4772
C) 0.9772
D) 0.9228

Answer 1

The probability that X is greater than 80 in a normal distribution with a mean of 100 and a standard deviation of 10 is 0.9772, which corresponds to option C.

Step-by-step explanation:

The student asks about determining the probability that a randomly selected score (X) from a normal distribution with a mean of 100 and a standard deviation of 10 is greater than 80. To find this probability, we first need to convert the score of 80 to a Z-score, which is a standard normal distribution score. The formula to calculate the Z-score is Z = (X - mean) / standard deviation. Therefore, the Z-score for 80 is:

Z = (80 - 100) / 10 = -2

Now we can use the standard normal distribution table or a calculator to find the probability that Z is greater than -2. This probability corresponds to the area under the standard normal curve to the right of Z = -2. Referring to a standard normal distribution table, or using a calculator with a normal distribution function, we find that the probability of Z being greater than -2 is approximately 0.9772, making option C the correct answer.