Question

The foreman of a bottling plant has observed that the amount of soda in each 30-ounce bottle is actually a normally distributed random variable, with a mean of 30.3 ounces and a standard deviation of 0.28 ounce. If a customer buys a carton of six bottles, what is the probability that the mean amount of the six bottles will be greater than 30 ounces? a. 0.9956 b. 0.8577 c. 0.1423 d. 0.0044

Answer 1

Given,

= 30.3

= 0.28

If a customer buys a carton of six bottle

i.e n = 6

Noe calculate p(x > 30)

p(x> 30) = 0.5 + p(0 < z < x-/(/n))

= 0.5 + p(0 < z < 30-30.3/(0.28/6))

= 0.5 + p(0 < z < -2.62)

= 0.5 + 0.4956

p(x > 30) = 0.9956

Hence option (a) is correct.