Question

Normal & Standard Normal Distribution



1. According to an article published on the Web site, Facebook users spend an average of 190 minutes per month checking and updating their Facebook pages. Suppose that the current distribution of time spent per month checking and updating a member’s Facebook page is normally distributed with a mean of 190 minutes and a standard deviation of 53.4 minutes. For a randomly selected Facebook member, determine the probability that the amount of time that he or she spends per month checking and updating his or her Facebook page is;

a. more than 300 minutes
b. between 120 and 180 minutes

2. According to a survey, Malaysian spend an average of 225 minutes per day communicating electronically (on a fixed landline phone, on a mobile phone, by emailing, by texting, and so on). Assume that currently such times for all Malaysians are normally distributed with a mean of 225 minutes per day and a standard deviation of 62 minutes per day. What percentage of Malaysians communicate electronically for;

a. less than 60 minutes per day
b. more than 360 minutes per day
c. between 120 and 180 minutes per day
d. between 240 and 300 minutes per day

Answer 1

Given:

Mean, = 190

Standard deviation, = 53.4

Let X : Malaysians communicate electronically.

X follows the Normal distribution.

X ~ Normal (=190, ^2=53.4)



Therefore the probability that

a) less than 60 minutes per day is 0.0039

b) more than 360 minutes per day is 0.0146

c) between 120 and 180 minutes per day is 0.1872

d) between 240 and 300 minutes per day is 0.2921

(All values are calculated from z table)