An independent third party found the cost of a basic car repair service for a local magazine. the mean cost is $217.00 with a standard deviation of $11.40. which of the following repair costs would be considered an “unusual” cost?
a.
$233.87
b.
$221.65
c.
$192.53
d.
$197.24

In this problem, the approach to solve the unusual value is to assume that the distribution used is a normal distribution. A normal distribution assumes that the mean is equal to zero, the area under the curve is 1 and that the standard deviation is equal to 1. In this case, we use the given mean and standard deviation to determine their corresponding ranges.

First range: mean +- SD
x1 = 217 + 11.4 = 228.4
x2 = 217 - 11.4 = 205.6
This only eliminates one option hence we move next to 2SD

Second range: mean +-2SD 
x1 = 217 + 2*11.4 = 239.8
x2 = 217 -2*11.4 = 194.2

This leaves option C not included in this range, hence C is the answer to this problem.

Sin(a)+cos(a)+cot(a)-1=2(csc(x)+1)