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:
[tex]z=\frac{x-m}{s}[/tex]
Where m is the mean and s is the standard deviation. So, the z-scores are calculated as:
[tex]z=\frac{54.2-65}{18}=-0.6\\ z=\frac{86.6-65}{18} =1.2[/tex]
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%
