The Famous Physicist, Ernest Rutherford, Was a Pioneer in the Study

Essay

The famous physicist, Ernest Rutherford, was a pioneer in the study of radioactivity using electricity. In one experiment he observed the number of particles reaching a counter during time 1,700 intervals of 7.5 seconds each. The number of intervals that had 0 - 4 particles reaching the counter is given in the table below. Let the random variable x = number of particles counted in a 7.5 second time period.
a) Fill in the table below with the estimated probability distribution of x, and sketch a probability histogram for x.
Probability histogram ​
b) Using the estimated probabilities in part (a), estimate the following: i) P(x = 1), the probability that 1 particle was counted in 7.5 seconds. ii) P(x < 3), the probability that fewer than 3 particles were counted. iii) P(x ≥ 3), the probability that at least 3 particles were counted.