1.a.The distribution of a particular IQ test scores for persons over 16 years of age is approximately Normal with mean 100 and standard deviation 17. What is the probability that a randomly chosen individual has an IQ score of 112 or higher? (Round your answer to four decimal places.)
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!
1.a.The distribution of a particular IQ test scores for persons over 16 years of age is approximately Normal with mean 100 and standard deviation 17.
What is the probability that a randomly chosen individual has an IQ score of 112 or higher? (Round your answer to four decimal places.)
b.The distribution of blood cholesterol level in the population of young men aged 20 to 34 years is close to Normal with standard deviation ? = 41 milligrams per deciliter (mg/dL). You measure the blood cholesterol of 15 cross-country runners. The mean level is x = 174 mg/dL. Assume that ? is the same as in the general population.
How large a sample is needed to cut the margin-of-error in half for a 90% confidence interval of the mean level ? among the cross-country runners?
c. Alysha makes 45% of her free throws. She takes five free throws in a game. If the shots are independent of each other, what is the probability that she makes exactly one of five shots? (Round your answer to three decimal places.)
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