Exercise Week 3

Individual Exercise 3 (10 points) 1. A shoe manufacturer’s data show that the distribution of shoe size is normal with a mean of 11inches and SD 1.5 inches. * A manger of the company claims that 70% of the times shoe size will be between 8 and 12 inches. What do you think? In your deliverables, write a few lines about what you think of the manager’s claim and what would you advise him to do. (1 point) * How would you modify the manager’s claim if the distribution of shoe size was not normal? (1 point). * What is (are) size(s) of shoe for which the probability of occurrence is less than or equal to 5%? In your deliverables, report the size. Explain in a few lines how you came to your conclusion. For this, assume shoe size is normally distributed. (2 points). 2. Those who apply for admission to OSU’s graduate college have to take and report their GMAT or GRE scores. In one population, GMAT scores are normally distributed with mean of 540 and s.d of 100, whereas GRE scores are normally distributed with a mean of 500 and s.d of 80. Who has a better score, a student with 600 on the GRE or a student with 660 on the GMAT? Why? (2 points).
Use the Comp data for answering the following questions. This data set has 222 observations (employee data from a company) and nine variables as described below:
Variable Name Description
Employee Number ID Identification numbers 1 to 222
Age Age Employee age in years
Gender SEX 0=male, 1=female
Annual Salary Salary Yearly wages in thousands of dollars
Prior Experience Prior Experience prior to joining this company (in years)
Education Educ 1 to 5 where 1=less than HS and 5=post graduate
Computer Expertise COMP 1=Expert, 0=not an expert
Grade Grade Job classification (1 to 6, 1=low, 6=high)
Experience EXPERI Experience at this company (in years)

3. Explore the distribution of the Age variable via histogram and moments. Overlay a Normal curve on the