Question

Assume that the traffic to the web site of Smiley’s People, Inc., which sells customized T-shirts, follows a normal distribution, with a mean of 4.56 million visitors per day and a standard deviation of 820,000 visitors per day.

(a)	What is the probability that the web site has fewer than 5 million visitors in a single day? If needed, round your answer to four decimal digits.
(b)	What is the probability that the web site has 3 million or more visitors in a single day? If needed, round your answer to four decimal digits.
(c)	What is the probability that the web site has between 3 million and 4 million visitors in a single day? If needed, round your answer to four decimal digits.
(d)	Assume that 85% of the time, the Smiley’s People web servers can handle the daily web traffic volume without purchasing additional server capacity. What is the amount of web traffic that will require Smiley’s People to purchase additional server capacity? If needed, round your answer to two decimal digits.
	million visitors per day

Answer 1

a)

The traffic to the web site of Smiley’s People, follows a normal distribution, with parameter

a)

The required probability is obtained by calculating the z score,

The probability is obtained from standard normal distribution table for Z = 0.5366

(In excel use function =NORM.S.DIST(0.5366,TRUE) )

b)

The probability is obtained from standard normal distribution table for Z = -1.9024

(In excel use function =1-NORM.S.DIST(-1.9024,TRUE) )

c)

(In excel use function =NORM.S.DIST(-0.6829,TRUE) - NORM.S.DIST(-1.9024,TRUE) )

d)

Since 85% of the time, the Smiley’s People web servers can handle the daily web traffic hence Smiley’s People will require 15% of the time to handle over capacity web traffic.

The z score for the over traffic probability, p = 0.15 is obtained from standard normal distribution table

For P=0.15, z = -1.036

(In excel use function =NORM.S.INV(0.15) )