A particle traveling through space which encounters a barrier is either transmitted (i.e., it goes through the barrier) or is reflected (i.e., it bounces back). For a certain type of particle and barrier, we know that 85% of particles are transmitted.
(a) If 60 particles encounter the barrier, and we are interested in the number of particles that are transmit ted, what is a good distribution to estimate that number? Include the parameters for that distribution.
(b) What is the expected value and standard deviation for the distribution identified in part a?
(c) Using the distribution identified in part a, what is an estimate for the probability that 55 or more particles are transmitted?
(d) Would a normal distribution adequately approximate this distribution? Explain why or why not. Regardless of your assessment of adequacy, calculate the probability from part b using the approxi mation. Is it close?