Probability Question for HW: Decision Sciences Class Need some help..?

Question

The average amount spent on back to school clothes was $527 in 2001 for children. Assume standard deviation is $160 and that the amount spent is normally distributed.

a)What is the probability that the amount spent on a randomly selected child is more than $700?

b) What is the probability that the amount spent on a randomly selected child iIs less than $100?

c) What is that probability that the amount spent on a randomly selected child is between $450 and $700?

Answer 1

Given mean μ=527 and SD σ=160 , so the standardized normal variate z= (x- μ)/σ,z=(x-27)/160

a)P(x>700)=?
x>700
=>160z+527>700
=> z>1.08125
P(z>1.08125) can be found from standard gaussian tables

b)P(x<100)=?
x<100
=> z>-2.66875
P(z>-2.66875) can be found from standard gaussian tables

c)P(450 => -0.48125 P(-0.48125

Answer 2

Using Z-tables,
a) Let a = (700 - 527)/160 ((x - μ)/σ)
Then P(x>700) = 1 - Z(a)

b) Let b = (100 - 527)/160
Then P(x<100) = Z(a)

c) Let b = (700 - 527)/160
and
a = (450 - 527)/160
Then P(450