There are two machines (M1 and M2) available for cutting corks intended for use in wine bottles. Machine M1 produces corks with diameters that are normally distributed with a mean of 3 cm and and a standard deviation of 0.06 cm. Machine M2 produces corks with diameters that have a normal distribution with a mean of 3.04 cm and a standard deviation of 0.02 cm?
a. If a cork is randomly selected from M1, what is the probability that the diameter of this cork is longer than 3.05 cm? Answer:
b. If a cork is randomly selected from M2, what is the probability that the diameter of this cork is longer than 3.05 cm? Answer:
c. If acceptable corks have diameters between 2.9 cm and 3.1 cm, compute the proportions of acceptable corks produced by M1 and M2. Answer for M1: , Answer for M2:
d. Which machine is more likely to produce an acceptable cork? Answer:
e.If 16 corks from M1 are randomly selected, what is the probability that the average diameter of these 16 corks is bigger than 3.05 cm? Answer: