Question

The time that customers wait to be served at the deli for a grocery store follows the uniform distribution between 0 and 7 minutes. What is the probability that a randomly selected customer will wait more than 4 minutes at the deli?.

Answer 1

The probability that a randomly selected customer will wait more than 4 minutes at the deli is given below

• The probability that a randomly selected customer will wait more than 4 minutes = $0.4286$

The waiting time for the customers is uniformly distributed between 0 - 7 minutes

Consider a random variabe X that represents the waiting time of customers and uniformly distributed between 0-7 minutes

Therefore, the density function of X is determined as

$f(x) = \frac{1}{b-a}\\\\f(x) = \frac{1}{7-0}\\\\f(x) = \frac{1}{7}$

The probability that the customer will wait more than 4minutes,

$P(X>4) = \int\limits^7_4 f{x} \,dx\\\\= \int\limits^7_4 \, \frac{1}{7}dx\\\\= \frac{1}{7} * [x]^7_4\\\\= \frac{7-4}{7} \\\\= 0.4286$

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