Question

Assume the random variable x is normally distributed with mean mu = 87 and standard deviation sigma = 4. Find the indicated probability. P(74 < x < 83) P(74 < x < 83) =

Answer 1

To find the probability, calculate the z-scores for the given values and use the standard normal distribution table or a calculator.

Step-by-step explanation:

Calculation and Graph:

To find the probability, we need to calculate the z-scores for the given values and use the standard normal distribution table or a calculator.

First, calculate the z-score for 74: z-score = (74 - 87) / 4 = -3.25

Then, calculate the z-score for 83: z-score = (83 - 87) / 4 = -1

Using the standard normal distribution table or a calculator, find the area corresponding to the z-scores:

P(74 < x < 83) = P(-3.25 < z < -1) = 0.0314

Step-by-step explanation:

The probability that x is between 74 and 83 is approximately 0.0314.