Your customers at the local bookstore spend time in the store browsing and buying. Assume this time is a uniform distribution from 3 minutes to 23 minutes. What is the height of the distribution? What is the standard deviation? A random customer enters the store 7 minutes before you are scheduled to leave, but your boss will not let you rush customers out the door. What is the probability you will be able to leave on time? Your boss at the local bookstore is interested in the mean amount spent by your customers. He remembers hearing about sampling and how it can help in these situations, but he also notes there must be a strong positive skew in the population distribution of money spent by customers, and he remembers sampling has something to do with normal distributions so he is not convinced it will work here. What important statistical concept is your boss forgetting about? Briefly explain this concept in your own words and how it applies here. Remember, your boss thinks he is a busy man, so you have to be brief.
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!
- Your customers at the local bookstore spend time in the store browsing and buying. Assume this time is a uniform distribution from 3 minutes to 23 minutes.
- What is the height of the distribution?
- What is the standard deviation?
- A random customer enters the store 7 minutes before you are scheduled to leave, but your boss will not let you rush customers out the door. What is the probability you will be able to leave on time?
- Your boss at the local bookstore is interested in the mean amount spent by your customers. He remembers hearing about sampling and how it can help in these situations, but he also notes there must be a strong positive skew in the population distribution of money spent by customers, and he remembers sampling has something to do with
normal distributions so he is not convinced it will work here.
- What important statistical concept is your boss forgetting about?
- Briefly explain this concept in your own words and how it applies here. Remember, your boss thinks he is a busy man, so you have to be brief.
Step by step
Solved in 4 steps