Statistics Discrete and Continuous Distributions

Statistics Discrete and Continuous Distributions

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Job Description

• The work needs to be clear and well organized.

• Clearly label each part of the project.

• Note, you can use Excel, Word, or do the project by paper and pencil / pen.

• You must show your work for the calculations. Simply providing an answer is not enough for the calculations. Please see the grading rubric for more information.


Normal Distribution
Jesse is curious to see what the possible daily demand will be for a new restaurant menu item. A similar meal item was introduced earlier in the year and its daily demand is normally distributed with a mean of 100 and a standard deviation of 25. Assume that the daily demand of the new menu item will also be normally distributed with a mean of 100 and a standard deviation of 25. Help Jesse determine the following probabilities and daily demand values.
1) Find the probability that daily demand will be between 110 and 130
2) Find the probability that daily demand will be between 80 and 120
3) Find the probability that daily demand will be greater than 130
4) Find the probability that daily demand will be less than 75
5) Find the probability that daily demand will be less than 90 or greater than 120
6) Find the value (let’s call it D) where the probability is 0.40 that demand will be less than this value
7) Find the value (let’s call it D) where the probability is 0.80 that demand will be greater than this value


Binomial
Alan is reviewing the outstanding bills that have not been paid by his customers. Alan usually gives his customers 30 days to pay a bill. After 30 days the bill is deemed late. Assume the probability is 30% that a customer will be late in paying a bill. For the next 15 bills that Alan reviews, find the following probabilities:
1) The probability that five will be late
2) The probability that at least five, but not more than ten will be late
3) The probability that more than three, but less than nine will be late
4) The probability that less than seven will be late
5) The probability that eight or more will be late
6) The expected number of late bills


Poisson
Katie is curious about the number of people entering her store over a half hour period. Suppose that on average six people enter her store every 30 minutes. Help Katie determine the following probabilities:

1) That exactly six customers will enter the store over the next 30 minutes
2) That less than five customers will enter the store over the next 30 minutes
3) That at least eight, but less than thirteen customers will enter the store over the next 30 minutes
4) That more than nine customers will enter the store over the next 30 minutes


Exponential Distribution.

Suppose the time between arrivals of customers at a store follows an exponential distribution with a mean of three minutes. Determine the following probabilities.

1) The time between arrivals is no more than seven minutes
2) The time between arrivals is between three and six minutes
3) The time between arrivals is greater than four minutes