1. Suppose a supermarket is conducting a survey to find out the busiest time and day for shoppers. Survey respondents are asked 1) whether they shopped at the store on a weekday or on the weekend and 2) whether they shopped at the store before or after 5 p.m. The survey revealed that

* 48% of shoppers visited the store before 5 p.m.

* 27% of shoppers visited the store on a weekday (Mon-Fri)

* 7% of shoppers visited the store before 5 pm on a weekday.

1) Construct a contingency table to summarize this data.

2) Calculate the probability that a respondent chosen at random is:

a. a shopper who shops before 5 p.m. on a weekend.

b. a shopper who shops on a weekend.

c. a shopper who shops after 5 p.m. on a week day.

d. a shopper who shops before 5 p.m. among the weekend shoppers.

e. a shopper who shops on a weekend among the shoppers who shops before 5 p.m.

2. Assume that the Illinois Lottery has hired you as a consultant to design a new pick-5 game where they wish to draw 5 letters out of a bucket that contains 26 letters of an alphabet regardless of the order of letter. Once a letter is picked, it will not be replaced.

1) Identify the probability of picking a winning combination of 5 letters.

2) Suppose that you have matched first 2 out of 5 letters. Three more letters are to be picked. What is the probability of you being the winner?

3. AT&T claims that when customers call directory assistance for telephone numbers, the right number is given 90% of the time. Assuming that the information is correct and we select 20 customers to request the directory assistant to AT&T. Answer the following questions. Let’s define X as the number of correct numbers.

1) Calculate the mean, the variance and the standard deviation of X.

2) Draw the probability distribution graph using Minitab, and copy and paste the graph.

3) Find the probability that the number of correct response is 10.

4) Find the probability that the number of correct response is at least 16 times out of 20 tries.

4. In a customer support center, there are average of 12 customers who are waiting in line. Let’s define X is the number of customers in the waiting line, and it has a Poisson distribution.

1) Calculate the mean, the variance and the standard deviation of X.

2) Draw the probability distribution graph using Minitab, and copy and paste the graph.

3) Find the probability that at least 8 customers are waiting to be answered.

4) Find the probability that there are more than 5 customers are waiting in the line

5. Some job satisfaction assessments are standardized to a Normal distribution with a mean of 100 and a standard deviation of 12.

1) Draw the probability distribution graph using Minitab, and copy and paste the graph.

2) What is the probability of people whose job satisfaction scores above 124?

3) What is the probability of people whose job satisfaction scores between 64 and 76?

4) What is the probability of people whose job satisfaction scores above 95?

6. Every normal distribution is defined by its parameters, the mean and the standard deviation. For each model described here, find the missing parameter.

1) µ = 1250, 35% below 1200; σ = ?

2) µ = 0.64, 12% below 0.70; σ = ?

3) σ = 0.5, 90% above 10.0; = µ ?

4) σ = 220, 3% below 202; µ = ?

7. Here are the two important two labor market indexes. (2 points)

YEAR |
FRBLMCI (X) |
UNEMP_RATE (Y) |

1992 |
1.4 |
7.5 |

1993 |
4.1 |
6.9 |

1994 |
6.1 |
6.1 |

1995 |
-1.9 |
5.6 |

1996 |
2.2 |
5.4 |

1997 |
4.7 |
4.9 |

1998 |
1.6 |
4.5 |

1999 |
3.3 |
4.2 |

2000 |
-1.8 |
4.0 |

2001 |
-16.3 |
4.7 |

2002 |
-1.4 |
5.8 |

2003 |
2.5 |
6.0 |

2004 |
7.2 |
5.5 |

2005 |
6.9 |
5.1 |

2006 |
4.0 |
4.6 |

2007 |
-1.6 |
4.6 |

2008 |
-19.2 |
5.8 |

2009 |
-9.7 |
9.3 |

2010 |
6.3 |
9.6 |

2011 |
6.2 |
8.9 |

2012 |
3.8 |
8.1 |

2013 |
4.1 |
7.4 |

FRBLMCI= Labor Market Conditions Index, Index, Annual

UNEMP_RATE= Civilian Unemployment Rate, Percent, Annual

1) Calculate the following statistics using Minitab and explain the central tendency of each statistic

Mean, Median, Q1, Q3

2) Calculate the following statistics using Minitab and explain the spread and shape of distribution.

Variance, Standard Deviation, Coefficient of Variation (CV), Skewness, Kurtosis

3) Make histogram for each index and confirm what you found from 1) and 2)

4) Calculate the following statistics using Minitab, and explain the relationship between two variables

Covariance between FRBLMCI and UNEMP_RATE

Correlation coefficient between FRBLMCI and UNEMP_RATE

5) Using any possible graph, illustrate the relationship between Unemployment and Labor market condition.

Subject | Mathematics |

Due By (Pacific Time) | 10/22/2014 12:00 am |

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