CNNBC recently reported that the mean annual cost of auto insurance is 950 dollars. Assume the standard deviation is 218 dollars, and the cost is normally distributed. You take a simple random sample of 9 auto insurance policies. Round your answers to 4 decimal places. b. What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N ( , ) ? c. What is the probability that one randomly selected auto insurance is less than $1016? d. a simple random sample of 9 auto insurance policies, find the probability that the average cost is less than $1016.
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!
CNNBC recently reported that the
b. What is the distribution of
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?
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~ N ( , ) ?
c. What is the probability that one randomly selected auto insurance is less than $1016?
d. a simple random sample of 9 auto insurance policies, find the probability that the average cost is less than $1016.
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