Stats - The Empirical Rule
About 95%
According to the empirical rule 68-95-99.7 rule, if a population has a normal distribution approximately what percentage of values is within two standard deviations of the mean?
The data is skewed to the left- cannot use the empirical rule
Biologists gather data on a sample of fish from a large lake. The sample is 1000 fish. The standard deviation is 5cm and the mean is 25 cm. They also notice that the shape of the distribution according to the histogram is very much skewed to the left, which means that some fish are smaller than most of the others. Approximately what percentage of fish in the lake is likely to have a length within one standard deviation of the mean?
The mean is 64 years The SD is 3.5 years. Two SD is (3.5)(2) = 7 years 64-7 = 57 years. Lower end of range 64 + 7= 71 years Approximate age range 57 to 71 years
If the average age of retirement for the entire population in a country is 64 years and the distribution is normal with a standard deviation of 3.5 years, what is the approximate age range in which 95% of people retire
48000-7000=41000 lower end of range 48000 + 7000=55000 upper end of range Normal distribution is symmetrical 34% of values between 41000 and 48000 and 34% of values between 48000 and 55000 50%+34% = 84% earn 55000 and below and 16% will earn above 55000
Last year's graduates from an engineering college who entered jobs as engineers had a mean first year income of $48000 with a standard deviation of $7000. The distribution of salary levels is normal. What is the approximate percentage of first year engineers that made more than $55000?
95% of the data lies within two standard deviations. 5% lies outside this range. (0.005)(600) = 30 lenses to be rejected.
The quality control specialists of a microscope company test the lens for every microscope to make sure the dimensions are correct. In one month 600 lenses are tested. The mean thickness is 2mm. The standard deviation is 0.000025 mm. The distribution is normal. The company rejects any lens that is more than two standard deviations from the mean. Approximately how many lenses outs of 600 would be rejected?
The empirical rule applies only if the distribution of the population is normal
What is a necessary condition for using the empirical rule 68-95-99.7 rule?
The mean and the standard deviation of the population
What measures need to be known to use the empirical 68-95-99.7 rule?