normal distribution A certain bank in the country has a clie

normal distribution

A certain bank in the country has a client charter that says among other things the waiting time for its customers before been attended to should not be more than 5 minutes. On a particular busy morning, the waiting times for its customers were recorded and found to be normally distributed with a mean of 4.8 minutes and a standard deviation of 2.4 minutes. i) How many percent of its customers on that particular morning have to wait for more than 5 minutes? ii) If 10% of its customers have to wait a minimum of k minutes, find the value of k precise to 3 significant figures.

Solution

(i) P(X>5) = P((X-mean)/s >(5-4.8)/2.4)

=P(Z>0.08) =0.4681 (from standard normal table)

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(ii)P(X>k)=0.1

--> P(Z<(k-4.8)/2.4) =1-0.1=0.9

--> (x-4.8)/2.4 =1.28 (from standard normal table)

So x= 4.8 +1.28*2.4 =7.8768