Question

Toyotas manufactured in the 1990s have a mean lifetime of 22.6 years, with a standard deviation of 3.1 years. the distribution of their lifetimes is not assumed to be symmetric. between what two lifetimes does chebyshev's theorem guarantee that we will find at least 95% of the toyotas? round your answers to the nearest hundredth. enter the bounds in ascending order.

Answer 1

Chebyshev's theorem guarantees that at least 95% of the Toyotas manufactured in the 1990s will have lifetimes between approximately 16.4 years and 28.8 years.

Step-by-step explanation:

According to Chebyshev's theorem, we can guarantee that at least 75% of the data lies within k standard deviations from the mean, where k is greater than 1. Therefore, to find the two lifetimes between which at least 95% of the Toyotas will be found, we need to determine the value of k. Since we want at least 95% of the data to be included, we subtract this value from 100% to get 5%. We divide this by 2 to get 2.5%. The corresponding k value that includes at least 97.5% of the data is 2. Therefore, we can say that between approximately 16.4 years and 28.8 years, we will find at least 95% of the Toyotas manufactured in the 1990s.