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 February 3rd, 2013, 06:30 PM #1 Member   Joined: Apr 2010 Posts: 33 Thanks: 0 Probability and Statistics Problem In a survey of 4000 cell phone users, we obtained that the mean time of cell phone usage is 35 minutes per day with a standard deviation of 5 minutes. Find the number of people (among total 4000) who will use a cell phone less than 40 minutes per day. (Assuming the distribution is bell-shaped and symmetric)
 February 3rd, 2013, 09:45 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond Re: Probability and Statistics Problem $\frac{1}{5\sqrt{2\pi}}\int_0^{40}\,e^{-\frac{(x\,-\,35)^2}{50}}\,dx\,\approx\,0.8413$ $0.8413\,\cdot\,4000\,\approx\,3365$
 February 4th, 2013, 08:23 AM #3 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond Re: Probability and Statistics Problem With $^{z}$ as the z-score, $^{\sigma}$ as standard deviation and $^{\mu}$ as the mean, we have $z\,=\,\frac{x\,-\,\mu}{\sigma}$ $z\,=\,\frac{40\,-\,35}{5}\,=\,1$ A z-score of 1 gives 84.13%, so the number of cell-phone users who use the phone less than 40 minutes per day is 0.8413 * 4000 ? 3365.

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