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Find the area under the standard normal curve between z=-1.57 and z=0.77. Round to four decimal...

Find the area under the standard normal curve between z=-1.57 and z=0.77. Round to four decimal places
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Answer #1

Let Z be a standard normal random number.

The area under the standard normal curve between z=-1.57 and z=0.77 is same as the probability that Z is between -1.57 and 0.77

P(-1.57 < Z < 0.77) = P(Z < 0.77) _ P(Z <-1.57) = P(Z < 0.77)-P(Z > 1.57] Due to the symmetry of standard normal distribution P(Z <-1.57)-P(Z > 1.57) = P(Z < 0.77)-[1-PlZ < 1.57)] total area under the curve s 1, and hence P(Z < 1.57) + P(Z > 1.57) = 1 or P(Z > 1.57)-1-P(Z < 1.57) = 0.7212 = (0.5+0.2794)-[1-(0.5 + 0.4418)] using standard normal tables for z=0.77 and z=1.57

ans: the area under the standard normal curve between z=-1.57 and z=0.77 is 0.7212

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