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In a busy day, 500 customers enter a store. The mean interarrival time is 0.4 minutes, and the standard deviation is 0.4 minutes.

1. What is the probability that the interarrival time will be less than 30 seconds (0.5 minutes) between customers?

Answer :

The probability that the interarrival time will be less than 0.5 minutes between customers is 0.5987.Answer:Thus, the probability the interarrival time will be less than 30 seconds (0.5 minutes) between customers is 0.5987.

In a busy day, 500 customers enter a store.Mean interarrival time is 0.4 minutes.Standard deviation is 0.4 minutes.The probability that the inter-arrival time will be less than 30 seconds between customers will be calculated as follows:Solution:To solve the problem, we can use the z-score formula which is:where, x = raw score, μ = population mean and σ = standard deviationThe given mean inter-arrival time = 0.4 minutes.To find the probability of inter-arrival time being less than 0.5 minutes, we convert it into a z-score using the formula as below. z=(x - μ) / σThe formula can be re-written as:x = μ + z × σFrom the problem,x = 0.5 minutes.μ = 0.4 minutes.σ = 0.4 minutes.z = (0.5 - 0.4) / 0.4z = 0.25The z-table shows that the probability corresponding to z-score 0.25 is 0.5987.

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