math stat. ch.3

which letter represents the​ median?

Letter B represents the median because roughly half of the values in the distribution are to the left of B and roughly half of the values in the distribution are to the right of B.

True or​ False: Chebyshev's inequality applies to all distributions regardless of​ shape, but the empirical rule holds only for distributions that are bell shaped.

True, Chebyshev's inequality is less precise than the empirical​ rule, but will work for any​ distribution, while the empirical rule only works for​ bell-shaped distributions. Recall that​ Chebyshev's inequality gives the minimum percent of the observations that lie within k standard deviations of the​ mean, while the empirical rule gives an approximation of the exact percent of the observations that lie within k standard deviations.

For a distribution that is skewed​ left, the left whisker is ......... the right whisker

longer than

For a distribution that is skewed​ left, which of the following is​ true?

mean (less than) < median

which letter represents the​ mode?

represents the mode because it is at the peak of the distribution

For a distribution that is​ symmetric, the left whisker is ....... as the right whisker

the same length as

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100100 and a standard deviation of 1616. Use the empirical rule to determine the following. ​(a) What percentage of people has an IQ score between 8484 and 116116​? ​(b) What percentage of people has an IQ score less than 8484 or greater than 116116​? ​(c) What percentage of people has an IQ score greater than 116116​?

a) = 68% b)= c)= ​· Approximately​ 68% of the data will lie within 1 standard deviation of the mean. ​· Approximately​ 95% of the data will lie within 2 standard deviations of the mean. ​· Approximately​ 99.7% of the data will lie within 3 standard deviations of the mean