# Normal Distribution help

• Mar 12th 2009, 08:42 PM
chardukian
Normal Distribution help
I am unsure how to finish this problem.
" The weekly amount spent by a company for travel has approximately a normal distribution with mean = $550 and standard deviation =$40. What is the probability that the actual expenses will exceed $570 in 20 or more weeks during the next year? (Suppose there are 52 weeks next year.) I know this is an approximation of normal distribution binomial but am unsure how to set it up. I started with z= x-550/40, but am unsure of the next steps to take. Can anyone help explain the next steps to take? Thanks. • Mar 12th 2009, 09:32 PM mr fantastic Quote: Originally Posted by chardukian I am unsure how to finish this problem. " The weekly amount spent by a company for travel has approximately a normal distribution with mean =$550 and standard deviation = $40. What is the probability that the actual expenses will exceed$570 in 20 or more weeks during the next year? (Suppose there are 52 weeks next year.)

I know this is an approximation of normal distribution binomial but am unsure how to set it up. I started with
z= x-550/40, but am unsure of the next steps to take. Can anyone help explain the next steps to take? Thanks.

Let X be the random variable amount spent (dollars) in a week.

X ~ Normal $\displaystyle (\mu = 550, \, \sigma = 40)$.

Calculate p = Pr(X > 570) = Pr(Z > 1/2).

Let Y be the random variable number of weeks in a year that exceed $570. Y ~ Binomial(p = calculated above, n = 52). Calculate$\displaystyle \Pr(Y \geq 20)\$. (The normal approximation is probably valid here).
• Mar 12th 2009, 10:14 PM
chardukian
Thanks a lot.