Q1 find the area under the normal curve to the right of z200

Q1: find the area under the normal curve to the right of z=2.00

Q2: find two z values correspond to the middle 48% of the area under the standard normal curve

Solution

Q1)

Area under the normal curve to the right of z=2.00

= P(z>2)

= 1- P(z<2)

= 1- 0.9772

= 0.0228 Answer

Q2)

The middle area of the standard normal curve is 48%.

So, the remaining areas (to the left of -z and to the right of z) is 52%.

The normal distribution is symmetric, the area to the left of -z is the same as the area to the right of z , each being 26% or 0.26.
This means the area below z (to the left of z) is 0.74.

From the normal probability table, find z such that P( z < ? ) = 0.74.
Look for 0.74 under the area and read z that corresponds to it.
The closes z is 0.64
Therefore, z-scores that separate the middle 48% of the distribution from the tails of standard normal distribution are :

- 0.64 and 0.64 Answer