Calculate the shaded area under the curve

Question

The shelf life of a batteries produced by one major company are normally distributed with a mean of 4.9 years and a standard deviation of 1 years. The figure below shows the distribution of shelf lives of batteries produced by one major company. Calculate the shaded area under the curve. Express your answer in decimal form with at least two decimal place accuracy.

Answer 1

Construct Z_3.9 = (3.9 − 4.9)/1 equal to -1/1 or -1.

Construct Z_6.9 =(6.9 − 4.9)/1 equal to 2/1 or 2.

An extremely accurate calculator program

for Proportions Of Area Under The Standard

Normal Curve gives p = -0.3413447461 for

Z_3.9 = -1.

The program gives p = 0.4772498681 for

Z_6.9 = 2.

Then take the shaded area under the curve as

0.4772498681 − -0.3413447461 which goes to

0.8185946141 or 0.82 to 2 decimal places.