Question

The temperature in a certain location was recorded each day for two months. The mean temperature was 84.9 degrees F with a standard deviation 2.5 degrees F. What can you determine about these data by using Chebyshev's Inequality with K = 3.

At least ___________% of the days had temperatures between _________ degrees F and _________ degrees F.
a) 55.56%, 77.4, 92.4
b) 77.78%, 77.4, 92.4
c) 88.89%, 77.4, 92.4
d) 66.67%, 77.4, 92.4

Answer 1

Chebyshev's Inequality states that a certain percentage of data falls within K standard deviations of the mean. Using K = 3, we can determine that at least 55.56% of the days had temperatures between the mean - 3 * standard deviation and mean + 3 * standard deviation.

Step-by-step explanation:

Chebyshev's Inequality states that for any data set, regardless of its shape or distribution, a certain percentage of the data will fall within K standard deviations of the mean. In this case, K = 3.

Using Chebyshev's Inequality, we can determine that at least 55.56% of the days had temperatures between mean - 3 * standard deviation and mean + 3 * standard deviation.

Therefore, the correct answer is a) 55.56%, 77.4, 92.4.