Alzheimers disease is a progressive, irreversible disorder, and at this time the

Question

Alzheimers disease is a progressive, irreversible disorder, and at this time the cause and cure are unknown. However, researchers at the University of Minnesota developed a brief, efficient and accurate means of predicting Alzheimers is persons from 65 to 85 years of age. The test takes about 10 minutes and requires the patient to try to recall 10 words after using each word twice in sentences. According to the researchers, the test results are accurate 95% of the time. If the test is administered to a random sample of 25 persons from 65 to 85 years of age, what is the probability that the test results are inaccurate for more than 12% of those persons sampled. Show your work and give your answer in the form of a sentence.

Explanation / Answer

Solution:- The probability that the test results are inaccurate for more than 12% of those persons sampled is 0.0341

The probability that test is accurate = 0.95

The probability that test is inaccurate = 1 - 0.95 = 0.05

Number of persons in the sample = 25

Number of persons to have inaccurate test results = 0.12 × 25 = 3

By applying binomial distribution:-

P(x, n, p) = nCx*px *(1 - p)(n - x)

P(x > 3) = 0.0341

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