Question

The following histogram displays the distribution of battery life (in hours) for a certain battery model used in cell phones: Suppose that battery life is a normal random variable with μ = 8 and σ = 1.2. Using the Standard Deviation Rule, what is the probability that a randomly chosen battery will last between 6.8 and 9.2 hours?

Answer 1

probably 68.27%

Explanation:

Answer 2

68.27%

Explanation:

An empirical rule for a normal distribution states that 68.27% of data is within 1 standard deviation (
`\sigma`) of the mean (
`\mu`), 95.45% of the data is within 2 standard deviations of the mean, and 99.73% of the data is within 3 standard deviations of the mean.

The problem asks for the probability that a battery will last between 6.8 and 9.2 hours considering that
`\mu`=8 and
`\sigma`=1.2.

So, if the distribution is normal, the 68.27% of data is within 1
`\sigma`, that is between
`\mu -\sigma` and
`\mu +\sigma`, replacing the values we have

8-1.2=6.8 and 8+1.2=9.2

So, 68.27% of batteries will last between 6.8 and 9.2 hours