The amount of fill in a half-liter (500 ml) soft drink bottle is normally distributed. The process has a standard deviation of 5 ml. The mean is adjustable.

a. Where should the mean be set to ensure a 95 percent probability that a half-liter bottle will not be underfilled?
b. Where should the mean be set to ensure a 99 percent probability that a half-liter bottle will not be underfilled?
c. Where should the mean be set to ensure a 99.9 percent probability that a half-liter bottle will not be underfilled?

A. 491.775

B. 488.37

C. 484.55

Step-by-step explanation:

A. 100-95 = 5

thus

using the formula;

where X = 500

         μ = mean

         σ = 5 (standard deviation)

   = 500 - 1.645(5)

   = 491.775

(please note that = 1.645 from the standard normal distribution table )

B. similarly,  following the above method we have

100 - 99 = 1

1/100 = 0.01

from the standard normal distribution table

 μ = X - σ

    = 500 - 2.326(5)

    = 488.37

C. 100 - 99.9 = 0.1

0.1/100 = 0.001

from the standard normal distribution

μ = X -  σ

   = 500 - 3.09(5)

    = 484.55

0.85 or 85%

step-by-step explanation:

1) divide 23 by 27

2) round the decimal to the nearest 10

3) so your answer would be 0.85 or 85%