The mean monthly utility bill for a sample of households in a city is $70, with a standard deviation of $8. Between what two values do about 95% of the data lie?

Answer: 95% of the data lies between $54 and $86

Use the Empirical Rule. The mean monthly utility bill for a sample of households in a city is $70, with a standard deviation of $8. Between what two values do about 95% of the data lie? (Assume the data set has a bell-shaped distribution.)

Step-by-step explanation:

Given;

Mean x = $70

Standard deviation r = $8

Confidence level = 95%

To determine the range of the data, we will solve using the confidence level of 95%

Using the formula

x + / - zr/√n

Where r = standard deviation and n is the number of samples tested.

But since n is not given, and since the distribution is bell shaped and thus normal.

The emprical rule states it about 95% of the data is within 2 standard deviations from the mean.

x+/-2r

Substituting x and r

$70 + / -2 (8)

$70 + / - $16

Which gives,

$54,$86

Therefore, 95% of the data lies between $54 and $86