6-29. Comment on the following : (a) The standard deviation of a distribution is invariant under changes of origin and scale. (0) j the mean and the standard deviation of n observations x, X2...., x bex and o respectively, the mean and standard deviation of-x,-x, ...-x, will be-x and-o respectively.

Part C. To reduce the percentage of defective chips the company...

ats 2. In the mid-19th century, Sir Francis Galton demonstrated, through extensive data collection, that many human characteristics such as height and IQ are distributed throughout the entire population in accordance with the normal distribution. Galton recorded the heights of 8585 men in Great Britain. This forms a normal distribution with a mean of 67 inches and standard deviation of 2.5 inches. (a) Graph this normal distribution and label the x-axis. (b) What proportion of these men were between 66 and 68 inches tall? belool vin (c) What fraction of the adult male population in Great Britain was within one standard deviation of the mean height? [Use the normal distribution function in Excel, not the Empirical Rule] (d) What height corresponds to the 95th percentile in the Galton study?

The graph illustrates the distribution of test scores taken by College Aigebra students. The maximum possible score on the test was 140, while the mean score was 76 and the standard deviation was 14. 34 48 62 76 90 104 Distribution of Test Scores What is the approximate percentage of students who scored between 76 and 90 on the test? What is the approximate percentage of students who scored higher than 104 on the test? What is the appraximate percentage of students who scored higher than 118 on the test? What is the approximate percentage of students who scored between 48 and 104 on the test?