Katie likes to shop at VONS. For each trip to the retail store, Katie spends an average of 44 mins with a standard deviation of 10 mins. The length of time spent in the store is normally distributed. Find the probability distribution that the shopper will be in the store for more than 30 minutes. Find the probability distribution that the shopper will be in the store between 35 minutes and 40 minutes.
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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Katie likes to shop at VONS. For each trip to the retail store, Katie spends an average of 44 mins with a standard deviation of 10 mins. The length of time spent in the store is
- Find the
probability distribution that the shopper will be in the store for more than 30 minutes. - Find the probability distribution that the shopper will be in the store between 35 minutes and 40 minutes.
- If 300 shoppers enter the store how many shoppers would you expect to be in the store for each time interval listed above (a,b).
- Interpret the results from a-c.
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