Question

The volume of a shampoo filled into a container is uniformly distributed between 370 and 385 milliliters. (a) What are the mean and standard deviation of the volume of shampoo? (b) What is the probability that the container is filled with less than the advertised target of 375 milliliters? (c) What is the volume of shampoo that is exceeded by 95% of the containers?

Answer 1

(a) mean = 377.5ml. standard deviation = 4.33

(b) 0.333

(c) 384.25 ml

Explanation:

(a)The mean:

`\mu = (385 + 370)/(2) = 377.5 ml`

The standard deviation:

`\sigma = (385 - 370)/(√(12)) = 4.33`

(b)

`P(x < 375) = (375 - 370)/(385 - 370) = (1)/(3) \approx 0.333`

(c)P(x > m) = 0.95

`(m - 370)/(385 - 370) = 0.95`

`m - 370 = 14.25`

`m = 384.25ml`

So the volumn of shampoo should be 384.25ml to exceed 95% of containers.