Question

Paula Pidcoe is doing her budget. She discovers that the average miscellaneous expense is $65.00 with a standard deviation of $18.00. What percent of her expenses in this category would she expect to fall between $54.20 and $86.60?

Answer 1

Answer:

61.06%

Step-by-step explanation:

First, we need to find the z-score for 54.2 and 86.6 using the following equation:

$z=\frac{x-m}{s}$

Where m is the mean and s is the standard deviation. So, the z-scores are calculated as:

$z=\frac{54.2-65}{18}=-0.6\\ z=\frac{86.6-65}{18} =1.2$

Finally, the percent of her expenses that she would expect to fall between $54.20 and $86.60 are calculated as:

P(54.2 < x < 86.6) = P(-0.6 < z < 1.2)

So, using the normal table, we get:

P(-0.6 < z < 1.2) = P(z < 1.2) - P(z < -0.6)

P(-0.6 < z < 1.2) = 0.8849 - 0.2743

P(-0.6 < z < 1.2) = 0.6106

The percent is 61.06%