Statistics
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RSCH665Assignment2.3.docx
RSCH 665 - Assignment 2.3
The table below will be used for the following five questions. The table represents the mean and standard deviation graduation rates, by candidate age, for a population of flight academies.
|
Age |
Mean Graduation Rate |
Standard Deviation |
|
16 |
76.6 |
1.8 |
|
17 |
74.2 |
1.8 |
|
18 |
79.5 |
1.7 |
|
19 |
79.6 |
2.1 |
|
20 |
81.2 |
2.1 |
|
21 |
84.2 |
2.2 |
|
22 |
85.5 |
2.1 |
|
23 |
88.5 |
1.4 |
|
24 |
86.5 |
1.5 |
|
25 |
87.7 |
1.9 |
|
26 |
87.8 |
1.5 |
|
27 |
88.1 |
1.6 |
|
28 |
89.8 |
1.8 |
|
29 |
90.1 |
1.8 |
|
30 |
87.8 |
2.3 |
|
31 |
88.3 |
2.2 |
|
32 |
88.3 |
1.7 |
|
33 |
84.5 |
1.9 |
|
34 |
85.1 |
1.6 |
|
35 |
88.1 |
1.4 |
|
36 |
88.2 |
1.5 |
|
37 |
86.5 |
1.4 |
|
38 |
84.5 |
1.8 |
|
39 |
88.8 |
1.9 |
|
40 |
84.4 |
1.6 |
1. A flight academy has a graduation rate of 72.1 among all their 17-year old candidates from the last five years. What percentage of flight academies have a higher graduation rate for 17-year old candidates?
Mean graduation rate of 17-year olds = 74.2, and std deviation = 1.8
P(X > 72.1)
= P(Z > (72.1 - 74.2)/1.8) (converting into the corresponding Z-score)
= P( Z > -1.167 )
= 0.879 = 87.9%
2. A flight academy has a graduation rate of 83.5 among all their 28-year old candidates from the last eight years. What percentage of flight academies have a lower graduation rate for 28-year old candidates?
Mean graduation rate of 28-year olds = 89.8, and std deviation = 1.8
Again, the graduation rate X can be considered to be normally distributed for large samples and hence,
P(X < 83.5)
= P(Z < (83.5 - 89.8) / 1.8)
= P(Z < -3.5)
= 0.0002 = 0.02%
3. A flight academy boasts it is among the top 10% for graduation rates among its 25-year old candidates. This academy’s graduation rate is 89.1 over the last two years for 25-year old candidates. Is the claim that this flight academy is in the top 10% a true statement? Explain.
4. A flight academy wants to invest in new training methods to improve its graduation rate of 18-year old candidates. This academy’s graduation rate for 18-year old candidates is 82.6 for the past ten years. Should the academy invest in the new training methods? Explain.
5. A flight academy had a graduation rate of 85.1 for 27-year old candidates from 2000-2009. Since then, new instructors have been hired that have specifically worked on providing clearer instruction to pilot candidates. From 2010-2018, the graduation rate for 27-year old candidates is 88.3. What percentile did the organization start at from 2000-2009, and what percentile is the organization now (2010-2018)? Explain what this means in terms of percentage of population between these scores.
