Suppose that you and two friends go to a restaurant, which last month filled approximately 91.1% of the orders correctly. Complete parts (a) through (d) below. Round to four decimal places as needed.) c. What is the probability that at least two of the three orders will be filled correctly? The probability is. (Round to four decimal places as needed.) d. What are the mean and standard deviation of the binomial distribution used in (a) through (c)? Interpret these values. The mean is. (Round to four decimal places as needed.) The standard deviation is. Round to four decimal places as needed.) Interpret the mean and standard deviation. Choose the correct answer below. O A. On average, 2.733 orders are correctly filled, while there is an approximate variation of 0.4932 from the average number of orders correctly filled. O B. On average, 0.4932 orders are correctly filled, while there is an approximate variation of 2.733 from the average number of orders correctly filled. O c. On average, 2.733 orders are correctly filled, while there is an approximate variation of 0.2216 from the average number of orders correctly filled. O D. On average, 0.7561 orders are correctly filled, while there is an approximate variation of 0.9777 from the average number of orders correctly filled.

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!