Consider the continuous random variable x, which has a uniform distribution over the interval from 110 to 150. The probability that x will take on a value between 120 and 125 is _____. A small business owner determines that her revenue during the next year should be approximately normally distributed with a mean of $425,000 and a standard deviation of $130,000. What is the probability that her revenue will exceed $600,000?
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!
Consider the continuous random variable x, which has a uniform distribution over the interval from 110 to 150. The
A small business owner determines that her revenue during the next year should be approximately
Suppose a preliminary screening is given to prospective student athletes at a university to determine whether they would qualify for a scholarship. The scores are approximately normal with a mean of 85 and a standard deviation of 20. If the
Given that z is a standard normal random variable, what is the value of z if the area to the right of z is .9370?
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