Answer :
The standard deviation of the amounts saved by Molly using coupons is [tex]\$2.68[/tex]
Molly's savings data: [tex]\$\ 6.00, \$\ 9.00, \$\ 3.00, \$\ 9.00, \$\ 3.00[/tex] hence [tex]n = 5[/tex]
- Find the mean of the savings:
[tex]\mu = \frac{\Sigma\ x_i}{n}[/tex]
[tex]\mu = \frac{6 +9 +3 + 9 + 3} {5} = 6[/tex] - Find the variance of the savings:
[tex]\sigma^2 = \frac{ \Sigma (x_i - \mu)^2}{n}[/tex]
[tex]\sigma^2 = \frac{ (6 - 6)^2 + (9-6)^2 + (3-6)^2 + (9-6)^2 + (3-6)^2}{5}[/tex]
[tex]\sigma^2 = \frac{0 + 9 + 9+ 9+ 9}{5} = \frac{36}{5}[/tex] - Calculate the standard deviation:
[tex]\sigma = \sqrt{\frac{36}{5}}[/tex]
[tex]\sigma = 2.68[/tex]
