The average age of college presidents is 56 years, with a standard deviation of 4 years. Assuming the ages are normally distributed, about what percentage of college presidents are between 56 and 59 years old?
77.34%
27.34%
84.13%
34.13%
65%
100%
To find the percentage of college presidents between 56 and 59 years old, we can calculate the z-scores for both ages using the formula:
z = (x - μ) / σ
Where x is the value of interest, μ is the mean, and σ is the standard deviation.
For 56 years old:
z₁ = (56 - 56) / 4 = 0
For 59 years old:
z₂ = (59 - 56) / 4 = 0.75
Next, we can use a standard normal distribution table or a calculator to find the percentage corresponding to each z-score.
For z = 0, the percentage is 50% (since it is the mean of a normal distribution).
For z = 0.75, the percentage is 77.34% (approximately).
To find the percentage of college presidents between 56 and 59 years old, we subtract the percentage corresponding to z₁ from the percentage corresponding to z₂.
Percentage = 77.34% - 50% = 27.34%
Therefore, approximately 27.34% of college presidents are between 56 and 59 years old. The correct answer is 27.34%.