Chapter 2.2, Problem 49E

(a)

To determine

To find: the proportion of observations from the standard normal distribution

Answer to Problem 49E

The proportion of observations is 0.8587

Explanation of Solution

Given:

z is between −1.33 and 1.65

Calculation:

The below standard normal possibilities table is a table of areas under the standard normal curve. The table entry for each value z is the area under the curve to the left of z.

  

  

From the Standard Normal probabilities table, the area to the left of = = 1.65is 0.9505 and the area to the left of z = -1.33 is 0.0918.

The area between z = -1.33 and z =1.65is the area to the left of 1.65 minus the area to the left of -1.33.

Therefore, the area between z =-1.33 & z =1.65 is 0.9505 - 0.0918 =0.8587. The result is shown in the below graph.

  

Conclusion:

The proportion of observations is 0.8587

(b)

To determine

To find: the proportion of observations from the standard normal distribution

Answer to Problem 49E

The proportion of observations is0.2718.

Explanation of Solution

Given:

z is between 0.50 and 1.79

Calculation:

From the Standard Normal probabilities table, the area to the left of $z=1.79$ is 0.9633 and the area to the left of z = 0.50 is 0.6915.

The area between z = 0.50 and z =1.79is the area to the left of 1.79 minus the area to the left of 0.50.

Therefore, the area between z = 0.50 & z =1.79 is 0.9633 - 0.6915 =0.2718. The result is shown in the below graph

  

Conclusion:

Therefore, proportion of observations is 0.2718.