Question

answer the question belowHow do you calculate a normal distribution área when shaded to the left of the mean?Write step by step

Answer 1

There are two possibilities when we calculate a normal distribution area. We need to calculate P(Z < z) where z is a negative number or P(Z < z) where z is a positive number.

If z is a negative number, for example, P(Z < -0.5), the value of z is to the left of the mean, so we can use the given table because that is the shaded area.

If z is a positive number, for example, P(Z < 0.3), we need to calculate the normal distribution area as:

1. Calculate P(Z < -0.3) as we say in the previous item

2. Then, calculate P(Z < 0.3) as 1 - P(Z < -0.3)

Finally, for the other probabilities, we need to write them to the form P(Z < z). For example

P(Z > 1.2) = 1 - P(Z < 1.2)

P(2.1 < Z < 2.5) = P(Z < 2.5) - P(Z < 2.1)