Introduction to Statistics

1. What is the probability of more than 3 phone calls per hour?

2. With current staffing plans, the bakery could handle up to 6 phone calls per hour during its busiest periods. What is the probability of more than 6 phone calls during one of the busy hours of the day? Is this a concern?

3. Where do we encounter Binomial or Poisson processes in everyday life?

4. Are there any tools in Excel to help us work with Binomial or Poisson distributions?

5. In what areas of your daily lives are normal curves used to describe things?

HINT: Remember - to find the probability of more than 3 calls you will need to use the concept of complimentary events, i.e. probability of more than 3 would be P(X>3) = 1 - P(X<=3)

Reopened one:

1.  What is the probability of more than 3 phone calls per hour?

The p of 3 calls per hour is .6406

   0=.01227

   1=.05402

   2=.118845

   3=.174305

       .35944

    1-.35944 = .6406 (rounded)

   I verified the answer using Stat Trek, which gave an answer of .6406 (rounded)

Meaning there is a 64% chance there will be more than 3 phone calls per hour.

2.  With current staffing plans, the bakery could handle up to 6 phone calls per hour during its busiest periods. What is the probability of more than 6 phone calls during one of the busy hours of the day? Is this a concern?

The p of 6 calls per hour is .1564 (rounded)

   (I omitted the list of calculations for this one)

   I verified the answer using Stat Trek

It is not a concern as the probability is low.  However, in practical application, an average of 4.4 means there are times when call volume is higher and lower.  More than 6 call per hour could be a problem, as it is possible as staff would not be able to handle high call volume times.  Again as the probability is low, only 16% chance of more than 6 phone calls per hour, a good, multi-tasking staff could handle this with minimal change to operations, added costs, or impact on customer service.

3.  Where do we encounter Binomial or Poisson processes in everyday life?

I like the binomial distribution as it is black and white; trials are either successful or failed.  The lottery is an example, either you win are going to win money, or you are not. 

For Poisson distributions, I think of sports, and how sports announcers love their statistics.  “Well Tom, it’s been 8 years since a hockey team in the Central Time Zone has won a game with more than 6 goals.  They have a 8% chance of winning by margin of 2 goals, if they are wearing blue jerseys.”   Then there is the popular gambling and sports betting, which can encompass both processes. 

4.  Are there any tools in Excel to help us work with Binomial or Poisson distributions?

I did not know that the formulas could be done in Excel, so this topic was good to research for me. 

Binomial Distribution: BINOMDIST(x, n, p, cum)

Note: n = the number of trials, p = the probability of success for each trial, cum = the value TRUE or FALSE.

Cumulative Probability Distribution:  BINOMDIST(x, n, p, TRUE)

Probability Density Function: BINOMDIST(x, n, p,  FALSE)

Poisson Distribution: POISSON(x, mu, cumulative)

5.  In what areas of your daily lives are normal curves used to describe things?

My normal commute home is 45 minutes because of traffic.  I know that if I make it home in 25 minutes it was highly unusual, but very much appreciated.  If it takes me an hour or more, it is also highly unusual, but aggravating none the less.

2-repoend two :

What is the probability of more than 3 phone calls per hour? 

P(>3) = .6406

While I did this via a ti83, the handout confirmed my calculations.

With current staffing plans, the bakery could handle up to 6 phone calls per hour during its busiest periods. What is the probability of more than 6 phone calls during one of the busy hours of the day? Is this a concern?

P(>6) = .1565

Again performed on the ti83 but the handout was a confirmation.

Statistically it’s within the usual standard deviations of occurrence though so being a concern is a subjective analysis. Is the bakery going to annoy patrons/lose business because of a 16% chance they can’t get to the phone or are people patient enough that when it happens you call back in a few minutes? Unless the expected worst case loss in sales, which would be another probability to calculate, is greater than the cost of hiring another staff person even just part time, then no no cause for concern.

Where do we encounter Binomial or Poisson processes in everyday life?

I do every morning about 5:45am. Do I get up or not? Within a standard deviation of 5min I’m usually within the normal parameters….

More realistically, for sporting events or patron turnover at a business, hospital admittance, etc. are examples, but nothing comes to mind that directly affects my day to day routine.

Are there any tools in Excel to help us work with Binomial or Poisson distributions?

There is a built in Poisson Distribution wizard. I prefer my ti83.

In what areas of your daily lives are normal curves used to describe things?

Framed like this maybe I misspoke about daily processes. One could look at normal sleep curves, eating habits, even uh regularity :).