Question

Find the area under the standard normal probability distribution between the following pairs of​ z-scores. a. zequals0 and zequals1.00 e. zequalsminus1.00 and zequals0 b. zequals0 and zequals2.00 f. zequalsminus2.00 and zequals0 c. zequals0 and zequals3.00 g. zequalsnegative 1.49 and zequals0 d. zequals0 and zequals0.82 h. zequalsminus0.82 and zequals0

Answer 1

See below

Explanation:

All this values can be easily found by using a table or a spreadsheet.

a)

P(0 ≤ z ≤ 1) = 0.3413

e)

P(-1 ≤ z ≤ 0) = P(0 ≤ z ≤ 1) = 0.3413 because N(0;1) is symmetrical

b)

P(0 ≤ z ≤ 2) = 0.4772

f)

P(-2 ≤ z ≤ 0) = P(0 ≤ z ≤ 2) = 0.4772

c)

P(0 ≤ z ≤ 3) = 0.4987

g)

P(-1.49 ≤ z ≤ 0) = 0.4319

d)

P(0 ≤ z ≤ 0.82) = 0.2939

h)

P(-0.82 ≤ z ≤ 0) = P(0 ≤ z ≤ 0.82) = 0.2939