PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 10.4, Problem 40E
Solution
a)
To verify: If the normal model can be used to describe the number of Type AB donors among 320 donors.
Yes, the normal model can be used to describe the number of Type AB donors among 320 donors.
Given:
The percentage of people having Type AB blood
The total number of donations collected
The number of Type AB donations among 320 donations
Concept used:
A probability distribution where each trial has two possible outcomes known as a success and failure, each trial is independent and the probability of each trial is the same, then to calculate the probability of a certain number of successes occurring, a binomial probability distribution is used. A binomial model can be approximated to be a normal model if it satisfies the following conditions
Calculation:
The total number of donations
The probability that people have type AB blood
The conditions to assume normal model are satisfied as shown below
Conclusion:
The conditions are satisfied, thus the number of Type AB donors can be assumed to be normally distributed.
b)
To calculate: The mean and standard deviation of the number of Type AB donors.
The mean and standard deviation of the number of donors is 12.8 and 3.5054 respectively.
Concept used:
The mean and standard deviation of the binomial model is calculated as shown below
Calculation:
The total number of donations
The probability that people have type AB blood
The mean and standard deviation are calculated as shown below
Conclusion:
The mean and standard deviation of the distribution of the number of Type AB donors is 12.8 and 3.5054 respectively.
c)
To calculate: Whether the outcome of 26 Type AB donors is statistically significant.
The outcome of 26 type AB donors is statistically significant.
Concept used:
The Z score, the number of standard deviations away from the mean is calculated using the formula
High values of the Z score are usually considered less likely to occur and statistically significant.Calculation:
The total number of donations
The probability that people have type AB blood
The number of people with Type AB blood
The Z score is calculated as shown below
Conclusion:
The Z score of 3.77 is very high and unusual. Thus the outcome of 26 type AB donors is statistically significant.
Chapter 10 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
Ch. 10.1 - Prob. 1QRCh. 10.1 - Prob. 2QRCh. 10.1 - Prob. 3QRCh. 10.1 - Prob. 4QRCh. 10.1 - Prob. 5QRCh. 10.1 - Prob. 6QRCh. 10.1 - Prob. 7QRCh. 10.1 - Prob. 8QRCh. 10.1 - Prob. 9QRCh. 10.1 - Prob. 10QR
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