Download Sec. 5.3 – Normal Distribution: Finding Values

Sec. 5.3 – Normal Distribution: Finding Values
Instead of finding an area or probability using the normal curve, you can also do the reverse:
find a z-score given the probability or area.
Find the z-score that corresponds to a cumulative area of 0.3632.
Find the z-score that has 10.75% of the distribution’s area to its right.
Find the z-score that corresponds to the given percentile, decile or quartile.
𝑃5
𝑄3
𝐷3
𝑃57
You can rewrite the z-score formula and solve for x. This will allow you to give an x-value for a
given z-score.
Remember: 𝑧 =
Therefore, 𝑥 =
The speeds of vehicles along a stretch of highway are normally distributed, with a mean of 67
miles per hour and a standard deviation of 4 miles per hour. Find the speeds 𝑥 corresponding to
z-scores of 1.96, -2.33, and 0. Interpret your results.
Scores for a civil service exam are normally distributed, with a mean of 75 and a standard
deviation of 6.5. To be eligible for civil service employment, you must score in the top 5%. What
is the lowest score you can earn and still be eligible for employment?
In a randomly selected sample of 1169 men ages 35-55, the mean total cholesterol level was
210 milligrams per deciliter with a standard deviation of 38.6 milligrams per deciliter. Assume
the total cholesterol levels are normally distributed. Find the highest total cholesterol level a
man in the 35-55 age group can have and be in the lowest 1%.