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Week Three

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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 manager 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)
The probability of a size being below size 8 is .02275 and the probability of a show size being size 12 or below is .747507. The probability of a size being between size 8 and 12 is .724732 or 72.4732%. * How would you modify the manager’s claim if the distribution of shoe size was not normal? (1 point).
I would change the claim to 75% and calculate the range using Chebychev’s Theorem. Using this theorem, 75% of the data should fall within 2 standard deviations of the mean, so the 75% of the time a shoe size would between size 8 and 14. * 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).
To calculate this we can calculate for 5% and 95% probability using Norm Inverse. This gives the number of 8.53272 and 13.46728. So a shoe size below 8.53272 or larger than 13.46728 has a probability of less than or equal to 5%. 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).
The GMAT student has a higher score since both scores are higher than…...

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