normal curve sketches

Question

Sketch the area under the standard normal curve over the indicated interval and find the specified area. (Round your answer to four decimal places.)

The area between z = −2.47 and z = −1.74 is

Answer 1

To find the area under the standard normal probability distribution function between two z values:

1. Find the area to the left of the larger z value z=-1.74. This can be done with a z-score table or a standard normal distribution calculator to find P(z<-1.74)=0.04093
2. Find the area to the left of the smaller z value z=-2.47: P(z<-2.47)=0.006755653
3. Subtract the number you get from step 1 by the number you get from step 2. This finds the area between z=-2.47 and z=-1.74 because the area to the left of -2.47 gets subtracted out. P(-2.47<z<-1.74)=0.04093-0.00676=0.0342

Sometimes they might want you to use rounded values for steps 1 and 2, or use the exact values from a calculator, which might affect the accuracy of your answer.