The average amount of money that people spend at Don Mcalds fast food place is $7.8600 with a standard deviation of $1.9800. 45 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. What is the distribution of XX? XX ~ N(,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,) What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
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!
The average amount of money that people spend at Don Mcalds fast food place is $7.8600 with a standard deviation of $1.9800. 45 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a
- What is the distribution of XX? XX ~ N(,)
- What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
- What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
- What is the probability that one randomly selected customer will spend less than $8.2272?
- For the 45 customers, find the probability that their average spent is more than $8.2272.
- Find the probability that the randomly selected 45 customers will spend less than $370.2240.
- For part e) and f), is the assumption of normal necessary? NoYes
- The owner of Don Mcalds gives a coupon for a free sundae to the 4% of all groups of 45 people who spend the most money. At least how much must a group of 45 spend in total to get the free sundae? $
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