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A Statistical Tutorial Centre has been designed to handle a maximum of 25 students per day. Suppose that the number X of students visiting this centre each day is a normal random variable with mean 15 and variance 16.

Part a) What is the return period for this centre rounded to the nearest day?


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Verified Answer :

A. return period =1/p 
where p= prob x>25 
Z=(x-mean)/stand dev, 
Recall stand dev = sqrt(variance) 
Z=(25-15)/4 
Z=2.5 which corresponds to .4938 
Prob of x>25=.5-.4938=.0062 
p=.0062 
1/p = 161.29 
161 days 

The return period for this center rounded to the nearest day is 161 days.

Calculation of the return period:

Since there is a maximum of 25 students per day. Suppose that the number X of students visiting this center each day is a normal random variable with mean 15 and variance 16.

So, we know that

Z=(x-mean)/stand deviation

Z=(25-15)/4

Z=2.5

=  .4938

Now

Prob of x>25=.5-.4938=.0062

p=.0062

1/p = 161.29

Hence, The return period for this center rounded to the nearest day is 161 days.

Learn more about variance here: https://brainly.com/question/24138432

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