PLEASE SHOW ALL WORK 10 Find the zscore boundaries that sepa

PLEASE SHOW ALL WORK

10) Find the z-score boundaries that separate a normal distribution as described in each of the following:

a) The middle 30% from the 70% in the tails

b) The middle 40% from the 60% in the tails

c) The middle 50% from the 50% in the tails

d) The middle 60% from the 40% in the tails

Solution

a)

Hence, by symmetry, the left tail has area 0.70/2 = 0.35.

Hence, using table/techology, the boundaries are

z = -0.385320466, 0.385320466 [ANSWER]

*************

b)

Hence, by symmetry, the left tail has area 0.60/2 = 0.30.

Hence, using table/techology, the boundaries are

z = -0.524400513, 0.524400513 [ANSWER]

*****************

c)

Hence, by symmetry, the left tail has area 0.50/2 = 0.25.

Hence, using table/techology, the boundaries are

z = -0.67448975, 0.67448975 [ANSWER]

********************

d)

Hence, by symmetry, the left tail has area 0.40/2 = 0.25.

Hence, using table/techology, the boundaries are

z = -0.841621234, 0.841621234 [ANSWER]