48. SUPERMARKET LINES A study of the checkout lines at Dwyer's Farms reveals that the probability that any one of ten checkout lanes is busy at an instant during peak hours is .8. a. What is the most probable number of checkout lanes that are busy at any instant? Hint: P(X = x) will continue to increase as long as P(X = x + 1) ? P(X = x). b. What is the probability that the number of checkout lines found in part (a) occurs?
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This is a binomial distribution with parameters n = 10 (number of lanes) and p = 0.8 (probability of a lane being busy). The probability mass function (PMF) for a binomial distribution is given by: P(X = x) = C(n, x) * p^x * (1-p)^(n-x) where C(n, x) is the Show more…
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