Question

Average talk time between charges of a given cell phone is advertised as 4 hours. Let the standard deviation be 0.8 hours. Use Chebyshev's Theorem to approximate the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours.

Answer 1

3/4

Explanation:

Answer 2

At least 3/4 of the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours.

Explanation:

Chebyshev's Theorem states that:

1) at least 3/4 of the data lie within two standard deviations of the mean, that is, in the interval with endpoints x bar ±2s for samples and with endpoints μ±2σ for populations;

2) at least 8/9 of the data lie within three standard deviations of the mean, that is, in the interval with endpoints x bar ±3s for samples and with endpoints μ ± 3σ for populations;

3) at least 1−1/k² of the data lie within k standard deviations of the mean, that is, in the interval with endpoints x bar ± ks for samples and with endpoints μ ± kσ for populations, where k is any positive whole number that is greater than 1.

1) endpoints μ ± 2σ for populations;

μ = mean = 4

σ = standard deviation = 0.8

= 4 ± 2(0.8)

= 4 ± 1.6

= 4+ 1.6 = 5.6

= 4 - 1.6 = 2.4

Therefore, the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours is at least 3/4