Let z be a normal random variable with mean 0 and standard deviation 1.What is P(1.3

Question

Let z be a normal random variable with mean 0 and standard deviation 1.What is P(1.3 < z < 2.3)?

Quizplus · Accepted Answer

The probability that z falls between 1.3 and 2.3 can be found using the standard normal distribution table or a calculator designed for statistics. The area under the standard normal curve to the left of z = 2.3 minus the area to the left of z = 1.3 gives the probability of z falling between these two values. Looking up these values in the standard normal distribution table or using a calculator, we find P(z < 2.3) ≈ 0.9893 and P(z < 1.3) ≈ 0.9032. Subtracting these gives 0.9893 - 0.9032 = 0.0861, which is the probability of z falling between 1.3 and 2.3.

Let Z Be a Normal Random Variable with Mean 0