Question

A sample of 11 years is taken. About how many are expected to have an ftes of 1,014 or above? Explain how you determined your answer.

a) 3
b) 5
c) 8
d) 11

Answer 1

Approximately 50% of the 11 years in the sample are expected to have an FTES of 1,014 or above. Option B is correct.

Step-by-step explanation:

To determine approximately how many of the 11 years in the sample are expected to have an FTES (full-time equivalent number of students) of 1,014 or above, we'll use the given information:

Population FTES median = 1,014 FTES

Population standard deviation = 474 FTES

We can assume that the FTES follows a normal distribution. Therefore, we'll use the concept of z-scores to calculate the probability:

First, we need to calculate the z-score for 1,014 FTES:

z = (x - μ) / σ

where x is the value we're interested in, μ is the population median, and σ is the population standard deviation.

z = (1,014 - 1,014) / 474 = 0

Using a table or a calculator, we can find that the area to the left of a z-score of 0 is 0.5.

Since we're interested in the number of years with an FTES of 1,014 or above, we want to find the area to the right of the z-score (1 - 0.5 = 0.5).

Therefore, approximately 0.5 (or 50%) of the 11 years in the sample are expected to have an FTES of 1,014 or above.