Question

erage of 420.5 miles on a full tank of gas. A researcher is interested in analyzing the data and finding z-scores and probabilities based on the given data. We will use cell referencing and Excel functions to find standardized z-scores and probabilities. We will apply the empirical rule to find intervals around the mean that include approximately 68%, 95%, and 99.7% of the data. Assume the mileage follows a normal distribution with a standard deviation of 50 miles. Use a cell reference or a single formula where appropriate in order to receive full credit. Do not copy and paste values or type values, unless otherwise directed, as you will not receive full credit for your answers.

Answer 1

- 68% of the data will be between 370.5 and 470.5 miles.

- 95% of the data will be between 320.5 and 520.5 miles.

- 99.7% of the data will be between 270.5 and 570.5 miles.

Explanation:

The 68-95-99 allows us to estimate quick intervals about a population knowing its mean and standard deviation.

By this rule, we can estimate that 68% of the population is within 1 standard deviation from the mean, 95% is within 2 standard deviations and 99.7 is within 3 standard deviations.

Then, 68% of the data will be between 370.5 and 470.5 miles.

`\mu-1\cdot \sigma=420.5-50=370.5\\\\\mu+1\cdot \sigma=420.5+50=470.5`

95% of the data will be between 320.5 and 520.5 miles.

`\mu-2\cdot \sigma=420.5-100=320.5\\\\\mu+2\cdot \sigma=420.5+100=520.5`

99.7% of the data will be between 270.5 and 570.5 miles.

`\mu-3\cdot \sigma=420.5-150=270.5\\\\\mu+3\cdot \sigma=420.5+150=570.5`