Question

The temperature in a certain location was recorded each day for two months. The mean temperature was 54.3F with a standard deviation1.9 F. What can you determine about these data by using Chebyshev's Inequality with K=3 ?

Answer 1

Explanation:

Chebyshev's inequality states that for any data set, regardless of the distribution, at least 1 - (1/K^2) of the data falls within K standard deviations of the mean.

In this case, K = 3, so we can apply Chebyshev's inequality to the temperature data with K = 3 to determine what percentage of the data falls within three standard deviations of the mean.

According to Chebyshev's inequality, at least 1 - (1/3^2) = 8/9 of the data falls within 3 standard deviations of the mean.

To calculate the range of temperatures that fall within three standard deviations of the mean, we can use the formula:

[mean - K * (standard deviation), mean + K * (standard deviation)]

Substituting the values given, we get:

[54.3 - 3 * 1.9, 54.3 + 3 * 1.9] = [48.6, 60.0]

Therefore, we can conclude that at least 8/9 of the temperature data falls within the range of 48.6°F to 60.0°F.