When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 972 comma 737 radioactive atoms, so 27 comma 263 atoms decayed during 365 days.

a. Find the mean number of radioactive atoms that decayed in a day.

b. Find the probability that on a given day, 51 radioactive atoms decayed.

You are in charge of the customer service phone line with many employees. at the end of each phone callthe customers are asked to rate their service from 1 to 5 stars, with 5 being the best. you find the averagerating for 20 randomly selected employees and decide you want to improve the ratings so you require thoseemployees to go through a new training program. you then wait a week and find the new average rating foreach employee. the average change is an increase in 1.3 stars with a standard devation of .9 stars.(a) is this data paired or not paired? (b) what are the null and alternative hypothesis being tested? (c) what is the t-statistic you would use? write the general formula and the final calculation.(d) sketch a t-distribution, label your t-statistic and the probability you would be interested in: