Hey all,

I have a question that I am not sure how to solve.

The firm Colddrinks produces a new kind of orange juice in bottles with label “contains 50 ounces of real juice”. The machine filling the bottles with orange juice follows a normally distributed process with µ =50.30 ounces and =0.30 ounces.
The daily production of bottles amounts to 5000. The quality department inspects 20 randomly chosen bottles each day. If more than two bottles contain less than 50 ounces of juice, the machine must be calibrated which costs the firm $3000. Calculate the probability that C will have to pay this cost. What is the expected cost to pay?

How would you solve it ?
I would calculate the prob for one bottle to countain less to 50 ounces (normal distribution with z = 1, prob = 15.87%)
And then a Bernoulli distribution with P(X=0) + P (x=1) , n = 20 and p = 0.1587, prob = 15,05%

Am I right ? and for the expected cost, multiply the prob by 3000.

Is this the right reasoning ? Thanks for correcting me if I am wrong