Question

In: Statistics and Probability

Determine the area under the standard normal curve that lies to the left of ​(a) Upper...

Determine the area under the standard normal curve that lies to the left of ​(a) Upper Z equals 0.53 comma ​(b) Upper Z equals 0.24​, ​(c) Upper Z equals 1.08​, and ​(d) Upper Z equals negative 1.39. ​(a) The area to the left of Zequals0.53 is

Solutions

Expert Solution

The area that lies below the Z score of a standard normal curve is the probability of the score that has the corresponding Z score.

This area can be calculated using the excel formula for normal distribution which takes the Z score as a parameter.

a) At Z = 0.53, the excel formula used is =NORM.S.DIST(0.53, TRUE), thus the probability score is computed as:

Probability = 0.7019

b) At Z = 0.0.24, the excel formula used is =NORM.S.DIST(0.24, TRUE), thus the probability score is computed as:

Probability = 0.5948

c) At Z = 1.08, the excel formula used is =NORM.S.DIST(1.08, TRUE), thus the probability score is computed as:

Probability = 0.8599

d) At Z = -1.39, the excel formula used is =NORM.S.DIST(-1.39, TRUE), thus the probability score is computed as:

Probability = 0.0823

The probabilities can also be calculated using the Z score table that is;


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