14 Aug Statistics
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
The graduation rate X can be considered to be normally distributed for large enough samples and hence,
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.
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