Answer:
The point estimate for the mean is 29.5 miles per gallon and the standard deviation is 5.9
Step-by-step explanation:
The formula por the point estimate of the mean is:
[tex]mean(x) = \frac{x1+x2+x3+...+xn}{n}[/tex]
And for the standard deviation:
[tex]desv(x)=(\frac{1}{n-1}sum(xi^{2} - n*x^{2} ))^{1/2}[/tex]
So for the mean:
[tex]mean(x)=\frac{33.6+26.8+20.2+38.7+35.1+28.0+26.2+27.6 }{8} \\\\mean(x)=\frac{236.2}{8} \\\\mean(x)=29.5[/tex]
And for the standard deviation:
[tex]desv(x)=(\frac{1}{8-1} ((33.6-29.5)^{2} +(26.8-29.5)^{2} +(20.2-29.5)^{2} +(38.7-29.5)^{2} +(35.1-29.5)^{2} +(28-29.5)^{2} +(26.2-29.5)^{2} +(27.6-29.5)^{2})^{1/2} \\\\desv(x)=(\frac{1}{8-1} ((4.1)^{2} +(-2.7)^{2} +(-9.3)^{2} +(9.2)^{2} +(5.6)^{2} +(-1.5)^{2} +(-3.3)^{2} +(-1.9)^{2})^{1/2} \\\\desv(x)=\sqrt{\frac{243.3}{7}} \\\\desv(x)=\sqrt{34.7} \\\\desv(x)=5.9[/tex]
