# MAT-Suppose that the arrival time of a patient to a doctor’s appointment

Suppose that the arrival time of a patient to a doctor’s appointment — relative to the original appointment time — is normally distributed with a mean of -5 minutes and a standard deviation of 5 minutes, for which positive values indicate the patient is late for their appointment. 1What is the probability that a randomly selected patient is late to his or her originally scheduled appointment?Report any equations or Excel functions that you use to answer this question.2What fraction of patients arrive no more than 12 minutes late? 3You are considering implementing a penalty: if a patient arrives more than k minutes late, they will have to pay \$25.What is the value ofk such that the penalty applies to no more than 2% of the patients?Please show work so I can understand how to do it.

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