Answer:
(a) mean = 377.5ml. standard deviation = 4.33
(b) 0.333
(c) 384.25 ml
Step-by-step explanation:
(a)The mean:
[tex]\mu = \frac{385 + 370}{2} = 377.5 ml[/tex]
The standard deviation:
[tex]\sigma = \frac{385 - 370}{\sqrt{12}} = 4.33[/tex]
(b)
[tex]P(x < 375) = \frac{375 - 370}{385 - 370} = \frac{1}{3} \approx 0.333[/tex]
(c)P(x > m) = 0.95
[tex]\frac{m - 370}{385 - 370} = 0.95 [/tex]
[tex]m - 370 = 14.25[/tex]
[tex]m = 384.25ml[/tex]
So the volumn of shampoo should be 384.25ml to exceed 95% of containers.
