At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .49. a. Find the probability that in a sample of 13 customers, none of the 13 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) Probability b. Find the probability that in a sample of 13 customers, at least 6 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) Probability c. Find the probability that in a sample of 13 customers, fewer than 7 will order a nonalcoholic beverage. (Round your answer to 4 decimal places.) Probability
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!
Given that:
At a Noodles and Company restaurant, the probability that a customer will order a non-alcoholic beverage is 0.49.
Sample size (n) = 13
Let X denote the number of customers who order a non-alcoholic beverage and X follows Binomial distribution with parameters and .
Probability mass function of Binomial variable X is given by the formula:
(a) To find the probability that in a sample of 13 customers, none of them will order a non-alcoholic beverage:
Required probability is obtained as follows:
Thus, the probability that none of them will order a non-alcoholic beverage is 0.0002
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