A binomial random experiment is conducted with 8 trials where the probability of success in each trial is p = 0.30. What is the probability of exactly 3 successes in these 8 trials? 0.419 0.254 0.211 0.296

Assume that random guesses are made for 8 ​multiple-choice questions on a test with 5 choices for each​ question, so that there are n=8 ​trials, each with probability of success​ (correct) given by p=0.20. Find the probability of no correct answers.

The president of Doerman Distributors, Inc., believes that 28% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers.  What is the probability that the sample proportion will be between 0.16 and 0.40 (to 4 decimals)? What is the probability that the sample proportion will be between 0.21 and 0.35 (to 4 decimals)?

Suppose that X is a binomial random variable with n = 10 and p = 0.29 . Find P( 5 ).Write only a number as your answer. Round to 4 decimal places (for example 0.1849). Do not write as a percentage.