Concept explainers
Heights of People The average height of a certain age group of people is 53 inches. The standard deviation is 4 inches. If the variable is normally distributed, find the
a. Greater than 59 inches
b. Less than 45 inches
c. Between 50 and 55 inches
d. Between 58 and 62 inches
(a)
To find: The probability that a selected individual’s height will be greater than 59 inches.
Answer to Problem 21CQ
The probability that a selected individual’s height will be greater than 59 inches is 0.0668.
Explanation of Solution
Given info:
The random variable
Calculation:
Use the z- score formula to convert the
The formula for the z- score is
Substitute the values in the above formula is as follows:
Thus, the value of
Use the Excel formula, to find the probabilities for specified z-value.
Thus, the
Conclusion:
There is a 0.0668 of chance that a selected individual’s height will be greater than 59 inches.
(b)
To find: The probability that a selected individual’s height will be less than 45 inches.
Answer to Problem 21CQ
The probability that a selected individual’s height will be less than 45 inches is 0.0228.
Explanation of Solution
Calculation:
Substitute the values in the z-score formula is as follows:
Thus, the value of
Use the Excel formula, to find the probabilities for specified z-value.
Thus, the
Conclusion:
There is a 0.0228 of chance that a selected individual’s height will be less than 45 inches.
(c)
To find: The probability that a selected individual’s height will be between 50 and 55 inches.
Answer to Problem 21CQ
The probability that a selected individual’s height will be Between 50 and 55 inches is 0.4648.
Explanation of Solution
Calculation:
Substitute the values in the z-score formula is as follows:
Thus, the value of
Use the Excel formula, to find the probabilities for specified z-value.
Thus, the
Conclusion:
There is a 0.4648 of chance that a selected individual’s height will be Between 50 and 55 inches.
(d)
To find: The probability that a selected individual’s height will between 58 and 62 inches.
Answer to Problem 21CQ
The probability that a selected individual’s height will be between 58 and 62 inches is 0.0934.
Explanation of Solution
Calculation:
Substitute the values in the z-score formula is as follows:
Thus, the value of
Use the Excel formula, to find the probabilities for specified z-value.
Thus, the
Conclusion:
There is a 0.0934 of chance that a selected individual’s height will be between 58 and 62 inches.
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Chapter 6 Solutions
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