Assume that a certain class is given a midterm examination. The
probability of a student studying for the examination is 0.6. Of those
students who study, the probability of their passing the examination is 0.9;
if a student does not study, his or her probability of passing is 0.05. Given
that a student did not pass the examination, what is the probability that
he or she studied? (5%)
Suppose that we want to estimate the true proportion of defectives in a
very large shipment of adobe bricks, and that we want to be at least 95%
confident that the error is at most 0.04. How large a sample will we need if
1. we have no idea what the true proportion might be; (5%)
2. we know that the true proportion does not exceed 0.1? (5%)
Let X be a Normal Distribution with mean 10 and standard deviation 4.
1. Find P(6 ≤ X ≤ 12) = ? (5%)
2. If P(X ≥ k) = 0.9332 , then k = ? (5%)
The following are the volumes, in deciliters, of 9 cans of peaches
distributed by a certain company: 46.2, 45.6, 46.6, 45.9, 45.7, 45.6, 46.7,
45.9, and 45.8. Assume the distribution of the volumes to be normal.
1. Find the sample variance s2 . (5%)
2. Find a 95% confidence interval for the mean. (5%)
3. Find a 95% confidence interval for the variance. (5%)
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