Statistics
Organize data for analysis in the form of graphs, tables, and frequency distributions.
Calculate statistical data for measures of central tendency and dispersion.
Investigate dispersion through normal distributions using range, mean, standard deviation, and zscores.
Measure location, variation, probabilities, distributions, and expectations.
[Adapted from “Real Statistics – Real Decisions”, Pg 221 of Larson, Elementary Statistics, 4th
Edition.]
Deadline
Due by Saturday at 11:59 pm, ET.
Directions
The Air Transport Association of America (ATA) is a
support organization for the principal U.S. airlines. Some of
the ATA’s activities include promoting the air transport
industry and conducting industry-wide studies. The ATA
also keeps statistics about commercial airline flights,
including those that involve accidents. From 1977 through
2006 for aircraft with 10 or more seats, there were 91 fatal
commercial airplane accidents involving U.S. airlines. The
distribution of these accidents is shown in the histogram at
the right.
1. Opening Paragraph – With every Weekly Case Study, you will begin by writing
an opening paragraph where you will summarize the statistical concepts you
have learned this week and describe how you plan to integrate those concepts
into this task.
2. In 2006, there were about 11 million commercial flights in the United States. If
one is selected at random, what is the probability that it involved a fatal accident?
3. Is a binomial distribution a good model for determining the probability of various
numbers of fatal accidents during a year? Explain your reasoning and include a
discussion of the four criteria for a binomial experiment. Make sure you clearly
think through each criterion.
4. Suppose that the probability of a fatal accident in a given year is 0.0000004.
Construct a binomial distribution for n = 11,000,000 and p = 0.0000004 (from
above) as well as p = 0.0000008 with x = 0 to 12.
x P(X = x)
P =
0.0000004
P(X = x)
P =
0.0000008
1
2
3
.
.
.
5. Using p = 0.0000004 in the above table, what is the probability that there will be:
(a) exactly 4 fatal accidents in a year?
(b) 10 fatal accidents?
(c) between 1 and 5, inclusive?
6. According to analysis by USA TODAY, air flight is so safe that a person “would
have to fly every day for more than 64,000 years before dying in an accident.”
How can such a statement be justified? Please include at least one reference to
an outside scholarly source (see Supplemental Syllabus for examples).
7. Metacognition – thinking about thinking and learning.
Please write a short paragraph (two to five sentences) explaining how you
will utilize the learning and thinking processes developed this week in
future assignments. In your reflection, not only address what worked, but
what did not work and why. How will you modify and hone your approach
for next week?