Normal Distribution Question

Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 4; σ = 2

P(3 ≤ x ≤ 7) 

Answer 1

Hi Been,

If we are trying to find 3 ≤ x ≤ 7 we can subtract µ and also divide by σ throughout the entire inequality:

(3 - 4) / 2 ≤ Z ≤ (7 - 4) / 2

-0.5 ≤ Z ≤ 1.5

The probability that lies between Z-scores of -0.5 and 1.5 can be found using a standard normal distribution table, or a handheld or online calculator. The probability is 0.6247.

Please let me know if I can be more helpful, thanks!

Joe