Any help offered in solving the below question will be much appreciated.
In a factory of metal plates, small dent occurs at random at an average of 1 dent in every 2 metal plates.
The number of dent detected in a metal plate is denoted by X and follows a Poisson distribution.
a) Show that, in a randomly chosen metal plate, the probability that there are at least 3 dents is 0.0144, correct to 3 Significant figures. (0.0144)
b) A box contains 15 such metal plates. Inspections are carried out at random to ensure quality. A box is rejected if it contains at least 2 metal plates with at least 3 dents each. Find the probability that a randomly chosen box is rejected. (0.0192)
c) 100 randomly chosen boxes are inspected. Find, by using a suitable approximation, the probability that more than 98 boxes are not rejected. (0.428) (Use Poisson Distribution to approximate Binomial Distribution)