Question

can i have help with problems 6 & 7?

6) (2 pts) A placement exam for entrance into a math class yields a mean of 80 and SD of 10. The distribution of the scores is roughly bell-shaped. use the Empirical Rule to find the percentage of scores that lie between 60 and 80. 7) (2 pts) The average number of newspapers for sale in an airport stand is 12. SD is 4. The average age of the pilots is 37 and SD is 6. Which data set is more variable? What are you going to use to answer this question?

Answer 1

6)

$\\Mean (\mu)= 80 \\Standard\;Deviation (\sigma)= 10 \\Since\; we\; know\; that \\z_{ score } = \frac{x-\mu}{\sigma} \\P(60.0 < x < 80.0)=? \\ z_1 = \frac {60.0-80.0}{10.0} \\ z_1 = -2.0 \\ z_2 = \frac {80.0-80.0}{10.0} \\ z_2 = 0.0\\ This\ implies\ that\\ P(60.0 < x < 80.0) = P(-2.0 < z < 0.0) = 0.4772$

7)

Coefficient of variation for data set (a)

$Coefficient\ of\ variation\ = \ \frac{4}{12}=0.33\\$

Coefficient of variation for data set (b)

6 Coefficient of variation = 0.162 12

Coefficient of variation of the data set ( b ) is less than that of the coefficient of variation of the data set ( a). Hence set ( a ) is more variable than set ( b ) .