A manufacturer of electroluminescent lamps knows that the amount of luminescent ink deposited on one of its products is normally distributed with a mean of 1.2 grams and a standard deviation of 0.03 grams. Any lamp with less than 1.14 grams of luminescent ink will fail to meet customer’s specifications. A random sample of 25 lamps is collected and the mass of luminescent ink on each is measured.

(a) What is the probability that at least 1 lamp fails to meet specifications?

(b) What is the probability that 5 lamps or fewer fail to meet specifications?

(c) What is the probability that all lamps conform to specifications?

(d) Why is the joint probability distribution of the 25 lamps not needed to answer the previous questions?