a.
To find:
The probability that a randomly selected student will drink less than suggested 40.5 oz of water in a day supposing the amounts of water that schoolchildren actually consume in a day are approximately
Answer to Problem 28E
Solution:
The probability that a randomly selected student will drink less than suggested water is 0.884.
Explanation of Solution
Given:
Mean
Standard deviation
Suggested intake according to report
Cut-off intake
Percentile
In statistics, 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 a given
which can be obtained from the normal distribution table.
The
or equivalently
Now,
In the first subpart, in order to find the probability the table is consulted to look-up the value in the row denoted by unit and tenth digits and the column by hundredth digit before which the
Calculation:
In the first part, using the given data and above relation:
that is:
which gives:
This
which is:
Rounding off to three places after the decimal, the probability is
Conclusion:
The probability that a randomly selected student will drink less than suggested water is 0.884.
b.
To find:
Amount by which the mean needs to be increased so that only
Answer to Problem 28E
Solution:
Amount by which the mean needs to be increased so that only
Explanation of Solution
Given:
Mean
Standard deviation
Suggested intake according to report
Cut-off intake
Percentile
Description:
In statistics, 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 a given
which can be obtained from the normal distribution table.
The
or equivalently
Now,
In the second part, the appropriate
Thereafter, the required increase in mean is computed.
Calculation:
In the second part, area on the left is equal to the decimal representation of percentile, that is:
From the table, the
Using the relation defined above,
the new mean is found as:
which gives the new mean:
Previous mean
Since thousandth place digit is 9 and
Conclusion:
Amount by which the mean needs to be increased so that only
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Chapter 6 Solutions
Beginning Statistics
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