Concept explainers
Longevity: 90th Birthday It is estimated that 3.5% of the general population will live past their 90th birthday (Statistical Abstract of the United States. 112th edition). In a graduating class of 753 high school seniors, what is the probability that
(a) 15 or more will live beyond their 90th birthday?
(b) 30 or more will live beyond their 90th birthday?
(c) between 25 and 35 will live beyond their 90th birthday?
(d) more than 40 will live beyond their 90th birthday?
(a)
To find: The probability that 15 or more will live beyond their 90th birthday.
Answer to Problem 9P
Solution: The probability
Explanation of Solution
Calculation:
Using
Thus,
The condition
Now, we calculate
Now, mean and standard deviation are as follows:
Further, the z-value corresponding to x is
Thus, the desired probability is 0.9906.
(b)
To find: The probability that 30 or more will live beyond their 90th birthday.
Answer to Problem 9P
Solution: The probability that 30 or more will live beyond their 90th birthday is 0.2676.
Explanation of Solution
Calculation: Using
Now, we calculate
Now, mean and standard deviation are as follows:
Further, the z-value corresponding to x is
Thus, the desired probability is 0.2676.
(c)
To find: The probability that between 25 and 35 will live beyond their 90th birthday.
Answer to Problem 9P
Solution: The probability that between 25 and 35 will live beyond their 90th birthday is
Explanation of Solution
Calculation:
Using
Now, we calculate
Now, mean and standard deviation are as follows:
Further,
Thus, the desired probability is 0.6092.
(d)
To find: The probability that more than 40 will live beyond their 90th birthday.
Answer to Problem 9P
Solution: The probability that more than 40 will live beyond their 90th birthday is
Explanation of Solution
Calculation:
Using
Now, we calculate
Now, mean and standard deviation are as follows:
Further, the z-value corresponding to x is
Thus, the desired probability is 0.0026.
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