Scores for a common standardized college aptitude test are normally distributed with a mean of 497 and a standard deviation of 107. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 545.5. P(X > 545.5) = Enter your answer as a number accurate to 4 decimal places. If 7 of the men are randomly selected, find the probability that their mean score is at least 545.5. P(M > 545.5) = Enter your answer as a number accurate to 4 decimal places. Assume that any probability less than 5% is sufficient evidence to conclude that the preparation course does help men do better. If the random sample of 7 men does result in a mean score of 545.5, is there strong evidence to support the claim that the course is actually effective? No. The probability indicates that it is too possible by chance alone to randomly select a group of students with a mean as high as 545.5. Yes. The probability indicates that it is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 545.5.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Scores for a common standardized college aptitude test are
If 1 of the men is randomly selected, find the
P(X > 545.5) =
Enter your answer as a number accurate to 4 decimal places.
If 7 of the men are randomly selected, find the probability that their mean score is at least 545.5.
P(M > 545.5) =
Enter your answer as a number accurate to 4 decimal places.
Assume that any probability less than 5% is sufficient evidence to conclude that the preparation course does help men do better. If the random sample of 7 men does result in a mean score of 545.5, is there strong evidence to support the claim that the course is actually effective?
- No. The probability indicates that it is too possible by chance alone to randomly select a group of students with a mean as high as 545.5.
- Yes. The probability indicates that it is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 545.5.
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