Chapter 2.2, Problem 48E

(a)

To determine

To find:

  $\text{z<-2}\text{.46}$

Answer to Problem 48E

Area (z < -2.46) = 0.0069.

Explanation of Solution

Given:

Use Table A to find the proportion of observations from the standard normal distribution that satisfies each of the following statements. In each case, sketch a standard normal curve and shade the area under the curve that is the answer to the question.

Calculation:

The below standard normal probabilities 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 z = -2.46 is 0.0069. Therefore, Area (z < -2.46) = 0.0069.

  

Conclusion:

Therefore, Area (z < -2.46) = 0.0069.

(b)

To determine

To calculate:

  $z>2.46$

Answer to Problem 48E

Area (z > 2.46) = 0.0069

Explanation of Solution

Given:

Use Table A to find the proportion of observations from the standard normal distribution that satisfies each of the following statements. In each case, sketch a standard normal curve and shade the area under the curve that is the answer to the question.

Calculation:

From the standard normal probabilities table, the area to the left of z = 2.46 is 0.991. Thus, the area to the right of z = 2.46 is 1 − 0.9931 = 0.0069.

Therefore, Area (z > 2.46) = 0.0069.

  

Conclusion:

Therefore, Area (z > 2.46) = 0.0069.

(c)

To determine

To find:

0.89 < z < 2.46

Answer to Problem 48E

The area between z = 0.89 ** z = 2.46 is 0.9931 − 0.8133 = 0.1798.

Explanation of Solution

Given:

Use Table A to find the proportion of observations from the standard normal distribution that satisfies each of the following statements. In each case, sketch a standard normal curve and shade the area under the curve that is the answer to the question.

Calculation:

From the Standard Normal probabilities table, the area to the left of - = 0,89is 0.8133 andthe area to the left of z = 2.46is 0.9931. The area between z = 2.46and z = 0.89 is the area to the left of 2.46 minus the area to the left of 0.89.

Therefore, the area between z=0.89 &z =2.46 is 0.9931 -0.8133 =0.1798.

  

Conclusion:

The area between z=0.89 &z =2.46 is 0.9931 -0.8133 =0.1798.

(d)

To determine

To find:

-2.95 < z < -1.27

Answer to Problem 48E

The area between z = -2.95 & z = -1.27 is 0.1020 - 0.0016 = [0.1004].

Explanation of Solution

Given:

Use Table A to find the proportion of observations from the standard normal distribution that satisfies each of the following statements. In each case, sketch a standard normal curve and shade the area under the curve that is the answer to the question.

Calculation:

From the Standard Normal probabilities table, the area to the left of z = -1.27is 0.1020and the area to the left of z = -2.95is 0.0016. The area between z=-2.95and z= -1.27is the area to the left of -1.27 minus the area to the left of -2.95.

Therefore, the area between z = -2.95 & z = -1.27 is 0.1020 - 0.0016 = 0.1004

  

Conclusion:

The area between z = -2.95 & z = -1.27 is 0.1020 - 0.0016 = 0.1004