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    Â
  P(X >   97   )          Â
=   P((x-µ)/σ >  ( 97 -  87) / 5)  Â
= Â Â P(Z Â > Â 2.00 Â Â ) Â Â Â Â Â Â Â Â Â Â
=   1-P( Z  ≤  2.00   )          Â
= Â Â 1 Â - 0.9772 Â Â Â Â Â Â Â Â Â
= Â Â 0.0228 Â Â Â Â Â Â Â Â Â Â Â Â Â Â
= Â Â 2.28% Â
Therefore, the probability that a randomly selected day's number of customers is more than 97 is 2.28%.
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