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?

Select one:

A. 0.8577

B. 0.1423

C. 0.0044

D. 0.9956

Answer 1

Given,

= 30.3

= 0.28

If a customer buys a carton of six bottle what is the probability that the mean amount of six bottle will be greater than 30 ounces?

Now 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 (D) is correct.

The probability that the mean amount of six bottle will be greater than 30 is 0.9956.