Concept explainers
(a)
To find: the proportion of observations from the standard
(a)
Answer to Problem 50E
The proportion of observations is 0.7621.
Explanation of Solution
Given:
z is between -2.05 and 0.78
Calculation:
The below Standard Normal probabilities table is a table of areas under the standard NormalCurve. 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 = 0.78 is 0.7823 andthe area to the left of z = -2.05 is 0.0202. The area between z = -2.05 and z = 0.78 is the area to the left of 0.78 minus the area to the left of -2.05.
Therefore, the area between z =-2.05 & z =0.78 is 0.7823 -0.0202 =0.7621. The result is shown in the below graph.
Conclusion:
The proportion of observations is 0.7621.
(b)
To find: the proportion of observations from the standard normal distribution
(b)
Answer to Problem 50E
The proportion of observations is 0.2410.
Explanation of Solution
Given:
z is between -1.11 and -0.32
Calculation:
From the Standard Normal probabilities table, the area to the left of z = -0.32is 0.3745and the area to the left of z = -1.11 is 0.1335. The area between z = -1.11 and z = -0.32 is the area to the left of -0.32 minus the area to the left of -1.11.
Therefore, the area between z = -1.11 & z=-0.32 is 0.3745-0.1335 =0.2410. The result is shown in the below graph.
Conclusion:
The proportion of observations is 0.2410.
Chapter 2 Solutions
The Practice of Statistics for AP - 4th Edition
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