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# Find the area under the normal curvea. To the left of z =

## Problem 2E Chapter 4.5

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 2E

Find the area under the normal curve

a. To the left of z = 0.56.

b. Between z = -2.93 and z = ‒2.06.

c. Between z = ‒1.08 and z = 0.70.

d. Outside z = 0.96 to z = 1.62.

Step-by-Step Solution:

Step 1 of 4:

Our goal is :

a). We need to find to the left of z=0.56.

b). We need to find between z=-2.93 and z=-2.06.

c). We need to find between z=-1.08 and z=0.70.

d). We need to find outside z=0.96 to z=1.62.

Now we have to find the area under normal curve.

a).

Given the area under standard normal curve to the left of z=0.56.

P(z<0.56)= P(z<0.56)

Using area under the normal curve table value.

P(z<0.56)= 0.7123

Therefore the area under standard normal curve to the left of z=0.56 is 0.7123.

Step 2 of 4:

b).

Given the area under standard normal curve between z=-2.93 and z=-2.06.

P(-2.93<z<-2.06)= P(z<-2.06)-P(z<-2.93)

Using area under the normal curve table value.

P(-2.93<z<-2.06)= 0.0197-0.0017

P(-2.93<z<-2.06)= 0.018

Therefore the area under standard normal curve between z=-2.93 and z=-2.06 is 0.018.

Step 3 of 4

Step 4 of 4

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