Question

Variable z follows the standard normal distribution. For each of the following, make a pencil sketch of the distribution & your finding. Using 5 decimals, find:

(a)[2] P(z ≤ ‐2.9);   [use NORM.S.DIST(•,1)]

(b)[2] P(z ≥ 2.4);   [elaborate, then use NORM.S.DIST(•,1)]

(c)[2] P(‐1.6 ≤ z ≤ 1.7);   [elaborate, then use NORM.S.DIST(•,1)]

(d)[2] z* so that P(z ≥ z*) = 0.07; [use NORM.S.INV(•)]

(e)[2] z** so that P(z ≤ z**) = 0.025. [use NORM.S.INV(•)]

Answer 1

The probability for Z score is calculated using the excel formula for normal distribution, the probability that is computed from the excel formula is the area from the left of the normal curve.

(a)P(z ≤ ‐2.9);   using =NORM.S.DIST(-2.9,TRUE), Thus the probability is computed as 0.00187, this can be plotted as:

(b)P(z ≥ 2.4); this the probability score above the Z-score 2.4 in the normal curve is calculated using the excel formula  =1-NORM.S.DIST(2.4,TRUE), thus the probability is computed as 0.00820.

This can be plotted as:

(c) P(‐1.6 ≤ z ≤ 1.7); the probability score btween the Z-score -1.6 and 1.7 of the normal curve is computed using the excel formula for normal distribution which is  =NORM.S.DIST(1.7, TRUE)-NORM.S.DIST(-1.6, TRUE), thus the probability is computed as 0.00964

This can be graphically plotted as:

(d) Given that P(z ≥ z*) = 0.07 the Z score corrosponding to the area or the probability is calculated using the excel formula for normal distribution which is =NORM.S.INV(1-0.07), Thus the probability score is calculated as 1.47579.

this can be plotted as:

(e)Given that P(z ≤ z**) = 0.025, the Z score corrosponding to the area or the probability is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.025), Thus the probability score is calculated as -1.95996.

This can be plotted as: