The probability that a randomly selected day's number of customers is more than 97 is 2.28%.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
As given, after collecting the data, Emma finds that the daily number of customers shopping at a small post office is normally distributed with mean 87 and standard deviation 5.
mean, µ= 87
standard deviation, σ= 5
Z = (x-µ)/σ
P(X > 97 )
= P((x-µ)/σ > ( 97 - 87) / 5)
= P(Z > 2.00 )
= 1-P( Z ≤ 2.00 )
= 1 - 0.9772
= 0.0228
= 2.28%
Therefore, the probability that a randomly selected day's number of customers is more than 97 is 2.28%.
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