Question

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)

Answer 1

The value of percentile at start is 3.01 while that of now is 55.17.

Explanation:

For the year the 2009 the value is given as 88.1 with a standard deviation of 1.6

Now for the value of 85.1 as of 2000-2009 the z score is given as

`z=(x-\mu)/(\sigma)\\z=(85.1-88.1)/(1.6)\\z=-1.88`

For this value of z, the P(z<x) is given as 0.0301. The corresponding percentile is 3.01.

Now for the value of 88.3 for 2010-2018, the z value is

`z=(x-\mu)/(\sigma)\\z=(88.3-88.1)/(1.6)\\z=0.13`

For this value of z, the P(z<x) is given as 0.5517 The corresponding percentile is 55.17.

The population between these two percentiles is given as 55.17-3.01 which given the value as 52.16.