Continuous Probablility Distributions...10pts!!?

Question

The average amount parents and children spent per chld on back-to-school clothes in Autumn 2001 was $527. Assume the standard deviation is $160 and the amount spent is normally distributed.

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

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

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

What is the probability that the amount spent on a randomly selected child is no more than $300?

Answer 1

You want to normalize the distribution so the the mean is zero and the variance is 1, you do this by the following formula

z = (x - mean)/(std dev), then you look at a standard normal table of values to see where the z is probability wise.

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

z = (700 -527)/160, so what is the probability the z>1.08
P(z>1.08) = 0.1401

second question, prob amount spent is less than $100
z=(100-527)/160 = -2.67
P(z<2.67) = 0.0038

You should have a general idea by now, get to know how the table in your book is set up, because they differ from book to book even though when read properly you get the same answer.

Answer 2

I used Excel to solve it.
--- --- ---
Probability that the amount spent is more than $700:
=1-NORMDIST(700; 527; 160; TRUE) ---> 13,98%

Probability that the amount spent is less than $100:
=NORMDIST(100; 527; 160; TRUE) ---> 0,3807%

Probability that the amount spent is btw $450 and $700:
=NORMDIST(700; 527; 160; TRUE)- NORMDIST(450; 527; 160; TRUE) ---> 54,50%

Probability that the amount spent is no more = less than $300:
=NORMDIST(300; 527; 160; TRUE) ---> 7,799%