Standard deviation

Question

Karen bought a book for $55. If book prices are normally distributed with a mean of $40 and standard deviation of $10, how many books (in terms of percentages of the total) are more expensive than the one Karen bought?

Answer 1

To determine how extreme your value given is, you need to find its z-score (how many standard deviations (σ) away from the mean (μ) it is)

z = (x-μ)/σ

z = (55 - 40)/10 = 1.5

 

You should either have a z-chart, or a way to calculate on your calculator, the area outside of the normal curve for each z-score. The value on the chart/calculator corresponding to z=1.50 is the value you're looking for. Multiply by 100% to find the percentage.