Section 5.3 . Normal Distributions: Finding Values. Examples 1 & 2. 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. Example 3 & 4.
Normal Distributions: Finding Values
The speeds of vehicles along a stretch of highway are normally distributed, with a mean of 56 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.
The monthly utility bills in a city are normally distributed, with a mean of $70 and a standard deviation of $8. Find the x-values that correspond to z-scores of -0.75, 4.29, and -1.82. What can you conclude?
bills that are lower than the
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?
be eligible for employment is 86.
The braking distances of a sample of Ford F-150s are normally distributed. On a dry surface, the mean braking distance was 158 feet and the standard deviation was 6.51 feet. What is the longest braking distance on a dry surface one of these Ford F-150s could have and still be in the top 1%?
distance on a dry surface
for an F-150 in the top 1%
is 143 ft.
In a randomly selected sample of 1169 men ages 35-44, the mean total cholesterol level was 205 milligrams per deciliter with a standard deviation of 39.2 milligrams per deciliter. Assume the total cholesterol levels are normally distributed. Find the highest total cholesterol level a man in this 35-44 age group can have and be in the lowest 1%.
of total cholesterol levels for men in the
35 – 44 age group from the highest 99%
is about 114.
The length of time employees have worked at a corporation is normally distributed, with a mean of 11.2 years and a standard deviation of 2.1 years. In a company cutback, the lowest 10% in seniority are laid off. What is the maximum length of time an employee could have worked and still be laid off?
employee could have worked and
still be laid off is 8.5 years.