Question

Use the empirical rule to solve the problem. The amount of Jen's monthly phone bill is normally distributed with a mean of $80 and a standard deviation of $8. What percentage of her phone bills are between $56 and $104? No need to insert percentage % sign. Round to one decimal?

Answer 1

The amount of Jen's monthly phone bill is normally distributed with a mean of =$80 and a standard deviation of =$8.

The empirical rule of standard deviation states that 66% of the values of a sample lies within +/-1 standard deviation, 95% of value lies within 2+/- standard deviation and 99.7% of values lie within +/-3 standard deviation.

This can be seen be pic shown below:

So, we need to find the standard deviation value at the $56 and $104 which is calculated as:

80+X*8=56

=> X=-3

again

80+X*8=104

=>X=3

So, from the empirical rule of standard deviation, 99.7% of values lie within the given $56 and $104.