Question

Given the normal distribution with a mean of 13 and a standard deviation of 4:

a. Find P(x < 17).
A) 0.1056
B) 0.3849
C) 0.8944
D) 0.6151

Answer 1

To find the probability that x is less than 17 in a normal distribution, calculate the z-score using the mean and standard deviation, then use a standard normal distribution table or calculator to find the corresponding probability.

Step-by-step explanation:

To find the probability that a random variable x is less than 17 in a normal distribution with a mean of 13 and a standard deviation of 4, we can calculate the z-score using the formula: z = (x - mean)/standard deviation. In this case, the z-score is (17 - 13)/4 = 1.

Using a standard normal distribution table or a calculator, the probability corresponding to a z-score of 1 is approximately 0.8413. Therefore, P(x < 17) is approximately 0.8413.

So, the correct answer is A) 0.1056.