Concept explainers
(a)
To find:
(a)
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
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 calculate:
(b)
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 find:
0.89 < z < 2.46
(c)
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 find:
-2.95 < z < -1.27
(d)
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
Chapter 2 Solutions
The Practice of Statistics for AP - 4th Edition
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