To find:
The
Answer to Problem 7CR
Solution:
The probability that the mean length of an adult blue whale from a random sample of 31 whales differs from the population mean by less than 2 meters is 0.9494.
Explanation of Solution
Given:
Formula:
In statistics, the normal
Where,
The normal Gaussian distribution with the following characteristics:
is called standard normal distribution with probability density function:
When this function is plotted on the
Area on the left of given
A normal distribution can be converted to standard normal distribution by defining the
Where
The area beyond two
It is noted that by Central Limit Theorem, that sampling distribution is approximately normal with:
a. mean
b. standard deviation
Initially the range of values within which the sample mean lies is found by subtracting and adding the difference from and to population mean.
Thereafter, the corresponding
Calculation:
Since the sample size follows the following condition:
The sample mean is given by:
And sample standard deviation is:
The range of values where the mean lies is:
Corresponding
And
Then, the area between the
Rounding off the number to
Conclusion:
The probability that the mean length of an adult blue whale from a random sample of 31 whales differs from the population mean by less than 2 meters is 0.9494.
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Chapter 7 Solutions
Beginning Statistics, 2nd Edition
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