Find the area under the standard normal distribution curve to the left of z=-2.15 and to the right of z=1.62

The area under the standard normal distribution represents probability from 0 to 1.
So, what's being asked, in essence, is what is P(Z ≤ -2.15) and P(Z ≥ 1.62).
P(Z ≤ -2.15) = 1 - P(Z ≤ 2.15) = 1 - 0.9842 = 0.0158.
P(Z ≥ 1.62) = 1 - P(Z ≤ 1.62) = 1 - 0.9474 = 0.0526

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fichoh fichoh · Answer 2 · 2021-11-06T05:40:07+01:00

Using the normal distribution table, which shows the percentage of the areas to the left a normal distribution, the area to the left z = - 2.15 and area to the right of z = 1.62 are 0.0158 and 0.0526 respectively.

1.)

The area under the normal distribution curve to the left of z = 2.15 can be expressed thus :

P(Z ≤ -2.15)

Using a normal distribution table ; the area to the left is

P(Z ≤ -2.15) = 0.0158

2.)

The area under the normal distribution curve to the right of z = 1.62 can be expressed thus :

P(Z ≥ 1.62) = 1 - P(Z ≤ 1.62)

Using a normal distribution table ; the area to the left is P(Z ≤ 1.62) = 0.94738

P(Z ≥ 1.62) = 1 - 0.94738 = 0.0526

Therefore, the area to the left z = - 2.15 and area to the right of z = 1.62 are 0.0158 and 0.0526 respectively.

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