# Thread: Help with Z scores and probabilities....

1. ## Help with Z scores and probabilities....

A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than ________% of minority students.

Assume that house prices in a neighborhood are normally distributed with standard deviation $20,000. A random sample of 16 observations is taken. What is the probability that the sample mean differs from the population mean by more than$5,000? For calculations, use your book table E.2.

I need to know how do to solve these. The answers have been given but i need to know how they got those asnwers.

For the first problem I think i need to figure the standard dev

I know for the second problem i need to use a z score but i dont know how to figure out the sample and population mean from the info given.

2. Originally Posted by Blevil
A study at a college in the west coast reveals that, historically, 45% of their students are minority students. If random samples of size 75 are selected, 80% of the samples will have less than ________% of minority students.

The number of minority students in a sample of $\displaystyle 75$ has a binomial distribution with mean $\displaystyle 0.45 \times 75$ and a standard deviation $\displaystyle \sqrt{75 \times 0.45 \times 0.55}$.

Now assume that the sample sizes are sufficient to use the normal approximation with the above mean and standard deviation.

CB

3. Thanks CaptainBlack

Im still not getting the answer I have ((75*.8)-(75*.45))/sqrt(75*.45*.55) <<< where am i going wrong?

4. Try this:

.845 = (x - 75*.45)/sqrt(75*.45*.55)

Once you solve for x you need to divide by the sample size of 75 to put it in % of minority students as the problem asks. The .845 on the left hand side of the equation comes from standard normal distribution corresponding to 80%.

5. .845 = (x - 75*.45)/sqrt(75*.45*.55)

ok so .845^2 = (x - 75*.45)/(75*.45*.55)

(.845^2)*(75*.45*.55)=(x - 75*.45)

so (.845^2)*(75*.45*.55) + (75*.45) = X << is this correct because i come with some weird number like 45.00 or something....darn im still stumped

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### a study of a college in the west coast reveals that, historically 45% of the students are minority students. if random samples of size 75 are selected, 80% of the samples will have less than % of minority students

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