Q:

A binomial experiment is conducted with 7trials. Each trial has a probability of 0.75 forsuccess.a) Which of these is a theoretical probability P(r)for r trialsi. P(2) = 0.012 iv. P(5) = 0.015ii. P(3) = 0.058 v. P(6) = 0.311iii. P(4) = 0.005b) What is the theoretical probability that at least4 of the trials are successful, rounded to threedecimal places?c) What is the theoretical probability that at most2 of the trials are successful, rounded to threedecimal places?

Accepted Solution

A:
Answer:Step-by-step explanation:To calculate the theoretical probability here, we need three inputs:  1) the number of trials (which here is 7); the probability of success (which here is 0.75); and an integer representing the particular outcome (which here would be r:  {0, 1, 2, 3, 4, 5, 6, 7}.(a)  Most of today's calculators have probability distribution functions built in.  I've used binompdf(n,p,r) here.  i. P(2) = 0.012 is correct; it's the result of typing in binompdf(7,0.75,2).  ii. P(3) = 0.058 is correct.  iii. P(4) = 0.005  is false; this probability is 0.173.  iv. P(5) = 0.015 is false.   v.  P(6) = 0.311 is correct.(b) The probability that at least four trials are successful is equivalent to P(4) + P(5) + P(6) + P(7).   Another way in which to calculate this would be to add up P(0) + P(1) + P(2) + P(3) and subtract the resulting sum from 1.00:  That comes to:  1 - (0.000 + 0.001 + 0.012 + 0.058), or 1 - 0.071, or 0.929