A manufacturing company takes a random sample of n = 100 bolts from their production line. X is the number of bolts that are found defective in the sample. It is known that the probability of a bolt being defective is 0.003. Does X have a binomial distribution? Yes. No, because the probability of success for each trial is not the same. No, because the trials are not all independent. No, because there is not a fixed number of trials. No, because there are more than two possible outcomes for each trial. OO O O

very morning, Laura practices shooting basketball free throws.  She doesn’t shoot a fixed amount, instead she keeps shooting free throws until she makes 12.  Suppose Laura is an 82% free throw shooter. Let X be how many free throws Laura will miss tomorrow morning.  Then X has a negative binomial distribution. What is a trial?                         What is a success?                         How many successes are required? r =                            What is the success probability?  p =

A company surveyed 2,600 North American airline passengers and reported that approximately 70% said that they carry a smartphone when they travel. Suppose that the actual percentage is 70%. Consider randomly selecting ten passengers and define the random variable x to be the number of the ten selected passengers who travel with a smartphone. The probability distribution of x is the binomial distribution with n = 10 and p = 0.7. (Round your answers to three decimal places.)     (a) Calculate p(8). p(8) = (b) Calculate P(x ≤ 6). P(x ≤ 6) = (c) Calculate the probability that more than half of the selected passengers travel with a smartphone.

Mike has a deck of standard poker cards with some cards missing. He wants to estimate the probability, p, of drawing a spade. Every day he makes an experiment. At the end of each experiment, he records the maximum likelihood estimator of the probability of observing a spade and places the drawn card back and shuffles the deck. Let X; be a random variable, taking value 1 if the i-th card draw of an experiment results in an even number and 0 if it results in an odd number. Clearly, X, ~ Bernoulli(p). Recall the MLE of a Bernoulli is p MLE The following are the outcomes of 5 experiments, one of which involved 8 card draws, two of which involved 6 card draws and two of which involved 4 card draws. Which experiments lead to the same MLE of p? Select all that apply. O (1 = 0, x2 = 1, r3 = 0, x4 = 0, r; 1, 6 = 0, x7 = 1, Is = 1, xg = 0, r10 = 1, 111 = 0, 112 = 0) O (1 = 1, a2 = 0, r3 = 1, x4 = 1) O ( = 0, x2 = 0, r3 = 0, r4 = 0) O (21 = 0, x2 = 1, £3 = 0, T4 = 0, x5 = 0, x6 = 0, r7 = 1, rg 0)…

A weighted coin has a 0.486 probability of landing on heads and a 0.514 probability of landing on tails. If you toss the coin 27 times, we want to know the probability of getting heads exactly 11 times.Consider a toss of heads as success in the binomial distribution.

What is the probability of getting at least a 3 star review, P(x≥3) ?

I. Boston Children’s Hospital estimates that 90% of Americans have had chickenpoxby the time they reach adulthood.32(a) Suppose we take a random sample of 100 American adults. Is the use of the binomial distributionappropriate for calculating the probability that exactly 97 out of 100 randomly sampled Americanadults had chickenpox during childhood? Explain.(b) Calculate the probability that exactly 97 out of 100 randomly sampled American adults had chickenpoxduring childhood.(c) What is the probability that exactly 3 out of a new sample of 100 American adults have not hadchickenpox in their childhood?(d) What is the probability that at least 1 out of 10 randomly sampled American adults have had chickenpox?(e) What is the probability that at most 3 out of 10 randomly sampled American adults have not hadchickenpox?

If the probability of a machine producing a defective part is 0.01, what is the probability of finding exactly 1 defective part from a sample of 10? (Assume that the process follows a binomial distribution)