# Math Help - Normal Distribution help

1. ## 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. 2. 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 $(\mu = 550, \, \sigma = 40)$.

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 $\Pr(Y \geq 20)$. (The normal approximation is probably valid here).

3. Thanks a lot.