In the following parts, you might suppose independence where it is reasonable to do so and is required to solve the problem.
a) A company is searching for the engineer to fill a new position. Assume that 15% of all potential applicants for the position would qualify for the personal interview. Applicants are considered sequentially. Compute the probability that the company has to consider more than twelve applicants to find out the first one who would qualify for interview? Compute to four decimal places.
b) Continuing part (a), assume that the company can only interview six candidates for position. Compute the mean number of applicants the company has to consider to find out six who would qualify for an interview?
c) The company is also searching for the biostatistician to fill an executive position. Assume that only 2% of all potential applicants meet all of the qualifications for this situation. The company decides to suggest 500 applicants. employ the Poisson distribution to approximate the probability that exactly eight applicants out of the 500 applicants will meet all of the qualifications. Calculate to four decimal place
d) The Poisson distribution in part (c) has the mgf: m(t)= e^10(e^t-1) . Use this mgf and differentiation to find the mean of this distribution. (Do not differentiate the general formula m(t)=e^λ(e^t-1). Please your work should be clear and complete with several detailed steps.