CNNBC recently reported that the mean annual cost of auto insurance is 955 dollars. Assume the standard deviation is 239 dollars. You take a simple random sample of 93 auto insurance policies. Give your answers as numbers accurate to 4 decimal places. a. Find the probability that a single randomly selected value is less than 984 dollars. b. Find the probability that a sample of size n = 93 is randomly selected with a mean less than 984 dollars.
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!
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