A random variable is normally distributed with a mean of ? = 80 and a standard deviation of ? = 5. a)The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 65 and 95). Sketch a normal curve for the probability density function. Label the horizontal axis with values of 65, 70, 75, 80, 85, 90, and 95. b)What is the probability the random variable will assume a value between 75 and 85? (Round your answer to three decimal places.) c)What is the probability the random variable will assume a value between 65 and 95? (Round your answer to three 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!
A random variable is
a)The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 65 and 95). Sketch a normal curve for the probability density
b)What is the probability the random variable will assume a value between 75 and 85? (Round your answer to three decimal places.)
c)What is the probability the random variable will assume a value between 65 and 95? (Round your answer to three decimal places.)
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