Question

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.)

Answer 1

95% of the data lies between $54 and $84

Explanation:

95% of data lies within 2 standard deviation on either side of the mean.

Lower value = mean-2SD = 70-2*8 = 70-16 = 54

Upper value = mean+2SD = 70+2*8 = 70+16 = 86

Then, 95% of the data lies between $54 and $84

Answer 2

Empirical rule dictates that, in a Bell-shaped distribution, 95% of data lies within 2 standard deviation on either side of the mean.

Therefore,
Lower value = mean-2SD = 70-2*8 = 70-16 = 54
Upper value = mean+2SD = 70+2*8 = 70+16 = 86

Then, 95% of the data lies between $54 and 84. These values can also be taken as the true mean of the population considering 95% confidence when sample mean has been calculated. In this regard, 2SD can be regarded as the margin error.