1. ACT University admission test results for ALL test takers are normally distributed – has one mode and symmetry. It has a mean equal to 18 and standard deviation is 6.2. Answer the following:
  1. University admitted students would have a median greater than or less than 18.

Greater than 18, assuming they admit the top scorers.

Why?

I assumed they admitted the top scorers.

  1. The shape of university admitted students is symmetric or skewed – if skewed, in what direction?

Skewed right, assuming they admit the top scorers.

  1. The standard deviation of university admitted student is greater, equal to or less than 6.2?

Less than 6.2, assuming thy admit the top scorers.

  1. Estimate the range of ACT for ALL test takers.

One of many practical estimates is 4 standard deviations. 4(6.2) = 24.8

  1. a. On January 1st 2000, the Cheyenne population was 30,000. On the same date in 2010, the population was 60,000. Determine the simple average annual growth rate and the GM growth rate for the population change.

Simple average growth rate = 100[(60,000 – 30,000) / (30,000(10))] = 10.00 %

Geometric mean growth rate = 100((60,000 / 30,000)^(1/10) – 1) = 7.18 %

b. A US Treasury bond has had the following returns for the past 5 years. Determine the proper annual average growth rate in enrollment.

.06, .07, -.03, .03, -.04

I will assume the question should read, “Determine the proper annual average return rate.”

(0.06 + 0.07 – 0.03 + 0.03 – 0.04)/5 = 0.018

  1. You are given the following data:

Mean / Median / Std Dev / Range / Sample Size / Skew/Sym
100 / 110 / 10 / ? / 25
100 / 90 / 15 / ? / 200
50 / 51 / ? / 30 / 10
150 / 150 / ? / 60 / 200
  1. Estimate the standard deviation and range where omitted.

Line 1: Range = 4(10) = 40

Line 2: Range = 4(15) = 60

Line 3: Standard deviation = 30/4 = 7.5

Line 4: Standard deviation = 60/4 = 15

  1. Determine the shape of the distribution – symmetric or skewed. If skewed, what direction

I will assume you are using the rule of thumb that determines skewness based on the mean and median relative values, even though it is not necessarily correct.

Line 1: Skewed left since the median is larger than the mean.

Line 2: Skewed right since the mean is larger than the median.

Line 3: Skewed left

Line 4: Symmetric

  1. LG 47 in TVs and Samsung 47 in TVs have the expected lives in the table below. If length of life is important to you, which manufacturer would you select.

Manufacturer / Mean / Median / Mode / StDev
LG / 6 / 5 / 4 / 2
Samsung / 3 / 6 / 8 / 2

The Samsung numbers are unusual.

I would choose LG with the larger mean and equivalent standard deviation.

  1. Use the data in the table below and determine the average hourly income across the three companies.

Company / Employees / Average Hourly Wage
GE / 80,000 / 22.50
IBM / 120,000 / 32.30
Microsoft / 140,000 / 35.80

[80,000(22.5) + 120,000(32.3) + 140,000(35.8)] / (80,000 + 120,000 + 140,000)

= $31.44