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.)
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