Answer :
Answer:
a) [tex]x \pm s = 484 \& 496[/tex]
b) [tex]x \pm 2s = 478 \& 502[/tex]
c) [tex]x \pm 3s= 472 \& 508[/tex]
Step-by-step explanation:
sample mean [tex](\overline{x})=490[/tex]
sample variance [tex](\overline{s}^2)=36[/tex]
sample standard deviation [tex](\overline{s}^2)[/tex] will be the square root of the sample variance:
[tex]\overline{s} = \sqrt{36} = 6[/tex]
Now we'll do our calculations:
a) [tex]x \pm s[/tex]
[tex]x \pm s = 490 \pm 6[/tex]
[tex]490 - 6\,\&\, 490 + 6 [/tex]
[tex]484 \& 496[/tex]
b) [tex]x \pm 2s[/tex]
[tex]x \pm 2s = 490 \pm 2(6)[/tex]
[tex]490 - 12\,\&\, 490 + 12[/tex]
[tex]478 \& 502[/tex]
c) [tex]x \pm 3s[/tex]
[tex]x \pm 3s = 490 \pm 3(6)[/tex]
[tex]490 - 18\,\&\, 490 + 18[/tex]
[tex]472 \& 508[/tex]