Question

The mean age of all high school teachers in New York state is 43 years and the standard deviation of their ages is 6 years. According to Chebyshev's theorem, the percentage of teachers in New York who are 31 to 55 years old is at least:

a. 0.77
b. 0.75
c. 0.70
d. 0.95

Answer 1

The percentage of high school teachers in New York who are 31 to 55 years old, according to Chebyshev's theorem, is at least 0.75.

Step-by-step explanation:

The percentage of high school teachers in New York who are 31 to 55 years old according to Chebyshev's theorem can be found by determining how many standard deviations away from the mean these ages are. Since Chebyshev's theorem guarantees that at least 75% of the data falls within two standard deviations from the mean, we can calculate the percentage as follows:

1. Find the distance of 31 years old from the mean: (31 - 43) / 6 = -2
2. Find the distance of 55 years old from the mean: (55 - 43) / 6 = 2
3. Since both values are within two standard deviations from the mean, we can be confident that at least 75% of the teachers' ages fall within this range.

Therefore, the correct answer is b. 0.75.