For Problems #1 through #11, consider the following context: The management of Café Ole runs

a reward or loyalty program specifically very frequent customers who visit their coffee shops

weekly. During a recent stormy week with very inclement weather, Chief Operations Officer

Maxine House was wondering if patron traffic among this very loyal group of customers was

diminished by bad weather. She gathered information from computerized cash register records,

and devised the following probability distribution table from relative frequency data about how

many days these customers stopped by and made purchases during that stormy week. Let x

represents the number of days during that calendar week these patrons visited the coffee shop

and bought products:

She forgot to enter the first and last probabilities but recalls that their values were identical.

Complete this probability distribution table and answer the following questions: [COMMENTS

& HINTS: Express all answer as percentages using the percent symbol. Ex: 1% or 99%.]

#1: Determine P(x = 0)

#2: Determine P(x = 7)

#3: Determine P(x < 2)

#4: Determine P(x \(\ge \) 3)

#5: Determine P(x \(\ne \) 4)

#6: What is the chance that a randomly selected patron from this frequent customer reward

program did not make exactly five (5) purchases?

#7: What is the chance that a randomly selected patron from this frequent customer reward

program made either three (3) or four (4) purchases?

#8: What is the chance that a randomly selected patron from this frequent customer reward

program made neither three (3) nor four (4) purchases?

#9: What is the chance that a randomly selected patron from this frequent customer reward

program stopped by to make purchases no more than two (2) times?

#10: What is the chance that a randomly selected patron from this frequent customer reward

program stopped by to make purchases at least five (5) days during this stormy week?

#11: On average, how many days did these patrons stop by to make purchases during this

stormy week? [COMMENTS & HINTS: What is the expectation or expected value for

this random variable? Express the answer rounded to the nearest whole number of days.

Enter only as a counting number: report approximately 8.49 days only as 8, or

approximately 9.50 days only as 10.]

#12: What is the shape of this probability distribution, based upon the percentages? [COMMENTS & HINTS: Select the most appropriate response.]

1. Bimodal
2. J-shaped
3. Rectangular or Uniform
4. Skewed Left or Negatively Skewed
5. Skewed Right or Positively Skewed
6. Symmetric or Triangular

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