Question

A machine adjusted to fill 330 ml of beverage has a normal distribution of 330 ml and a standard deviation of 5 ml, which is the average amount of beverage filled into bottles.

Amount of beverage filled,

i) If it is below 326 ml, with a probability of 0.03,

ii) 0.002 probability between 326 ml and 332 ml

iii) over 332 ml with a probability of 0.10

the machine will give an error signal.

a) What is the probability that the machine gives an error signal?

b) What is the probability that the machine has filled more than 332 ml of drinks when it is known that it gives a false signal?

c) 8 bottles are selected regardless of these drinks. What is the probability that more than 2 bottles are filled under 325 ml?

d) What is the probability that the average of the beverage amount will be more than 331 ml for another sample of 36 bottles randomly selected from these drinks?

Answer 1