1. Find the area under the standard normal curve (a) between -2.4 and 2.4 (b) be

Question

1. Find the area under the standard normal curve (a) between -2.4 and 2.4 (b) between 0 and 2.4 (c) between -2.4 and 0 (d) to the right of 2.4 (e) between 0 and 1.15 (f) between -2.4 and 1.15 (8) to the right of 1.15 (h) to the left of 1.15 2. The normal curve is sketched below. Solve for z in the following problems. 107. 3. A certain STAT 208 exam had scores that were notmally distributed, with an average of 60 points and a standard deviation (SD) of i5 points. Find the percent of students who have scores (a) between 45 and 75 points (f) under 55 points (b) betwee:: 30 and 90 points (g) over 50 points (c) between 50 and 65 points (b) under 65 points (d) between 65 and 95 points (i) ind the 25th percentile (e) over 90 pointe find the 90th percentile

Explanation / Answer

1)
from the standard right tailed z-table we can find the area greater than z = 2.4 i.e. P(Z>2.4) = 0.008197

P(Z > 1.15) = 0.1251

a) P(-2.4 < Z < 2.4) = 1 - 2*P(Z > 2.4) = 1 - 2*0.008197 = 0.9836

b) P(0 < Z < 2.4) = 0.5 - 0.008197 = 0.491803

c) P(-2.4 < Z < 0) = 0.5 - 0.008197 = 0.491803

d) P(Z > 2.4) = 0.008197

e) P(0 < Z < 1.15) = 0.5 - P(Z > 1.15) = 0.5 - 0.1251 = 0.3749

f) P(-2.4 < Z < 1.15) = 1 - P(Z > 2.4) - P(Z > 1.15) = 1 - 0.008197 - 0.1251 = 0.866703

g) P(Z > 1.15) = 0.1251

h) P(Z < 1.15) = 1 - P(Z > 1.15) = 1 - 0.1251 = 0.8749

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