Concept explainers
(a)
Find the z interval for
(a)
Answer to Problem 11P
The z interval for
Explanation of Solution
Calculation:
Z score:
The number of standard deviations the original measurement x is from the value of
In the formula, x is the raw score,
The variable x is red blood cell (RBC) count in millions per cubic millimetre for women. The healthy females are
For the z interval consider,
Subtract 4.8 on both sides of the inequality.
Divide 0.3 on both sides of the inequality.
Hence, the z interval for
(b)
Find the z interval for
(b)
Answer to Problem 11P
The z interval for
Explanation of Solution
Calculation:
For the z interval consider,
Subtract 4.8 on both sides of the inequality.
Divide 0.3 on both sides of the inequality.
Hence, the z interval for
(c)
Find the z interval for
(c)
Answer to Problem 11P
The z interval for
Explanation of Solution
Calculation:
For the z interval consider,
Subtract 4.8 for each part of the inequality.
Divide 4.3 for each part of the inequality.
Hence, the z interval for
(d)
Find the x interval for
(d)
Answer to Problem 11P
The x interval for
Explanation of Solution
Calculation:
The z score is,
For the x interval consider,
Multiply 0.3 on both sides of the inequality.
Add 4.8 on both sides of the inequality.
Hence, the x interval for
(e)
Find the x interval for
(e)
Answer to Problem 11P
The x interval for
Explanation of Solution
Calculation:
For the x interval consider,
Multiply 0.3 on both sides of the inequality.
Add 4.8 on both sides of the inequality.
Hence, the x interval for
(f)
Find the x interval for
(f)
Answer to Problem 11P
The x interval for
Explanation of Solution
Calculation:
For the x interval consider,
Multiply 0.3 for each part of the inequality.
Add 4.8 for each part of the inequality.
Hence, the x interval for
(g)
Identify whether the RBC count of 5.9 or higher can be considered unusually high or not using z values and Figure 6-15.
(g)
Answer to Problem 11P
The RBC count of 5.9 or higher is unusually high.
Explanation of Solution
Calculation:
The RBC count of 5.9 or higher, that is
Subtract 4.8 on both sides of the inequality.
Divide 0.3 on both sides of the inequality.
The RBC count of 5.9 or higher is 3.67 standard deviations above the mean value. The z score value is greater than 3 indicating that the value is very unusual.
The figure 6-15 is the standard normal distribution curve. The z value is located on the curve as below.
The z value that is far from the mean (zero) is considered as unusual. If the value is closer to –3 is usually very small and value closer to 3 is usually very large.
If the value of z for RBC count of 5.9 or higher is greater to 3 then RBC count would be very large and unusual.
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Chapter 6 Solutions
Understandable Statistics: Concepts and Methods
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