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
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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