14111cwir10ws.1 - enter normalcdf(left bound right bound...

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Fall 2011 Week-in-Review #10 courtesy: Kendra Kilmer (covering Sections 8.5, 8.6, and 5.1) Sections 8.5 and 8.6 If X is a continuous random variable , a probability density function is defined to represent the probability distribution of X . The curve lies completely above the x -axis and the total area under this curve is 1. A normal random variable is defined by its mean ( μ ) and standard deviation ( σ ). The probability density function associated with a normal random variable has its peak directly above the mean and is symmetric about a vertical line passing through the mean. The standard normal variable Z has a mean of 0 and a standard deviation of 1. To find probabilities associated with a Normal Random Variable, press 2nd VARS and the select option 2:normalcdf. On your homescreen,
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Unformatted text preview: enter normalcdf(left bound, right bound, mean, standard deviation). • If you are given a probability and asked to find a bound use 3:invNorm. If you are trying to find a , then a =invNorm(total area under the curve to the left of a , mean, standard deviation). 1. Let Z be the standard normal variable. Find the following: (a) P ( Z ≥ 1 . 5) (b) P ( Z < 2) (c) P (-1 . 5 < Z ≤ 2) 2. Let X be a normal random variable with μ = 80 and σ = 5. Find the following: (a) P ( X ≤ 70) (b) P ( X > 75) (c) P (45 ≤ X ≤ 90)...
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