Scores for a common standardized college aptitude test are normally distributed with a mean of 510 and a standard deviation of 111. Randomly selected men are given a Prepartion Course before taking this test. Assume, for sake of argument, that the Preparation Course has no effect on people's test scores. If 1 of the men is randomly selected, find the probability that his score is at least 543.3. P(X > 543.3) = Enter your answer as a number accurate to 4 decimal places. If 16 of the men are randomly selected, find the probability that their mean score is at least 543.3. P(x-bar > 543.3) = Enter your answer as a number accurate to 4 decimal places. If the random sample of 16 men does result in a mean score of 543.3, is there strong evidence to support a claim that the Preapartion Course is actually effective? (Use the criteria that "unusual" events have a probability of less than 5%.) No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 543.3 if the Preparation Course has no effect. Yes. The probability indicates that is is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 543.3 if the Preparation Course has no effect.
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 > 543.3) =
Enter your answer as a number accurate to 4 decimal places.
If 16 of the men are randomly selected, find the probability that their mean score is at least 543.3.
P(x-bar > 543.3) =
Enter your answer as a number accurate to 4 decimal places.
If the random sample of 16 men does result in a mean score of 543.3, is there strong evidence to support a claim that the Preapartion Course is actually effective? (Use the criteria that "unusual" events have a probability of less than 5%.)
- No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 543.3 if the Preparation Course has no effect.
- Yes. The probability indicates that is is highly unlikely that by chance, a randomly selected group of students would get a mean as high as 543.3 if the Preparation Course has no effect.
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