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Chapter 7: Problem 51

While the majority of people who are color blind are male, the National Eye Institute reports that \(0.5 \%\) of women of with Northern European ancestry have the common form of red-green color blindness. Suppose a random sample of 100 women with Northern European ancestry is selected. Can we find the probability that less than \(0.3 \%\) of the sample is color blind? If so, find the probability. If not, explain why this probability cannot be calculated.

Short Answer

Expert verified
No, the probability of less than 0.3% of these 100 women with Northern European ancestry being colorblind cannot be calculated using a binomial distribution because it involves a non-integer number of successes, which is impossible in this discrete model.

Step by step solution

01

Understanding the problem and identifying the given parameters

Here, the given parameters include the number of trials \(n\), which is the number of women sampled (100), and the probability of success \(p\), which is the likelihood of a woman having color blindness according to the National Eye Institute (0.005). However, the problem is asking for the probability of less than 0.3 percent of the women sampled being colorblind, which would be less than 1 woman since \(0.003 \times 100 = 0.3\) women. Since we can't have a fraction of a woman, this is not a value that we can use in the standard binomial formula.
02

Attempting to find the probability

While it would be possible to calculate the probability of exactly 0, 1, 2, etc. women being colorblind in the sample using the binomial formula, we cannot use it to find the probability of a fraction of a woman being colorblind. Therefore, we can't find this probability using a binomial distribution.
03

Final conclusion

The probability of less than 0.3% of these 100 women with Northern European ancestry being colorblind cannot be found using a binomial distribution because it would involve finding the probability of a non-integer, which is not possible with the discreet nature of this distribution model.

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