normal distribution

Question

Weekly wages at a certain factory are normally distributed with a mean of $400 and a standard deviation of $50. Find the probability that a worker selected at random makes between $450 and $500.

Answer 1

You should memorize thus rule: (from Wikipedia) "In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively. "

"a mean of $400 and a standard deviation of $50"

Between $350 to $450: 68.27% [one SD from 400]

Between $300-to $500: 95.45% [two SD from 400]

Now,,draw those if needed.. The percent (which represents probability) between one SD and two SD's [note: in either direction] is:

95.45% - 68.27% = 27.18%

The probability of being between $450 and $500 is half that .

P[$450 to $500) = 13.59%

Answer 2

Similar to a problem i just answered.

The range 450-500 is 50-100 from the mean, and with std dev of 50, this is 1-2 std devs away.

Statistical tables indicate 13.6% of the normal distribution will be between 1-2 std devs from the mean, in one direction. So the answer is 13.6%.