STAT 301 - Business Statistics
Lecture Review #7 - Normal Distribution

Review questions:

1) What are some examples of quantities that are typically normally distributed?

2) What proportion of the data in a normal distribution lies within one standard deviation of the mean? Within two standard deviations? Three?

Computational exercises:

1) Automated machinery is used to fill boxes of Chocolate Frosted Sugar Bombs breakfast cereal. The machine is calibrated to put an average of 16.4 ounces of cereal in each box. Minor variation in the process causes the standard deviation to be 0.2 ounces.

a) What percentage of the boxes of cereal weigh less than 16 ounces?

b) What percentage weigh between 16.2 and 16.8 ounces?

c) What percentage are more than 17.4 ounces?

2) A recent anthropological study of the aboriginal dwarf pygmies living on the island of Kafoonistan has shown that adult males in the tribe have an average height of 60", with a standard deviation of 4".

a) What percentage of the men of the tribe are over six feet (72") tall?

b) How tall are the tallest 10% of the men in the tribe?

c) How short are the shortest 20% of the men in the tribe?

3) Daily returns on the Boravian Stock Exchange (BSE) are normally distributed, with a mean of 0.1% and a standard deviation of 1.2%.

a) How often does the BSE gain 2% or more, in a given day?

b) What percentage of the time does the BSE drop in value (that is, have a return less than 0)?

c) What’s the chance that the BSE experiences returns between 0.5% and 1.5%, in a given day?

d) What’s the probability of a daily return of 5% or higher, on the BSE?

4) Students applying to law school are normally expected to take the Law School Admissions Test (LSAT). The test is similar to the SAT. Scores on the LSAT are scaled to be normally distributed with mean 150 and standard deviation 10.

a) What percentage of test-takers get between a 145 and a 155 on the LSAT?

b) Lawyer wannabe I.V. League aspires to an LSAT score in the top 10%. What score is needed to achieve this goal?

c) To be admitted to the Balph Snerdwell School of Law and Cosmetology, you need a score in the bottom 4.2% of the distribution. What score is needed to achieve this highly dubious goal?

d) Scores on the LSAT run from a low of 120 to a high of 180. Why are these the top and bottom scores?

SOLUTIONS:
1a) .0228   1b) .8185   1c) approx. 0
2a) .0013   2b) 65.12" or more   2c) 56.64" or less
3a) 0.057   3b) 0.467   3c) 0.248   3d) approx. 0
4a) 0.383   4b) 162.8 or higher   4c) 132.7 or less   4d) 3 sd’s from mean