Question

normal distribution help please

Answer 1

okay whats your problem?

Answer 2

A genius society requires an IQ that is in the top 2% of the population in order to join. If an IQ test has a mean of 100 and a standard deviation of 15, what is the minimum qualifying score to join the genius society?

Answer 3

holy cow. No idea bro

Answer 4

You're supposed to find \(k\) such that \(P(Y\le k)=0.98\). \(k\) is a test score, \(Y\) is a random variable denoting a possible score, and 0.98 refers to the fact that 98% of the scores lie to the left of \(k\).

First, transform the given distribution into the standard normal: \(Z=\dfrac{Y-\mu}{\sigma}\), where \(Z\) is the new random variable, \(\mu\) is the mean (100), and \(\sigma\) is the standard deviation (15).
\[P(Y\le k)=P(Z\sigma+\mu\le k)=P(15Z+100\le k)=0.98\]
Refer to a \(z\)-table to find the corresponding \(z\)-value: http://www.resourcesystemsconsulting.com/blog/z-table/

You'll see 0.98 gives \(z\) between 2.05 and 2.06; pick either one.
So now you have to solve the following:
\[15(2.05)+100\le k\]
This \(k\) will be the borderline score required to get into the "genius society."

Answer 5

If any of this isn't making sense, let me know.

Answer 6

that's a lot but I don't know where you got .98

Answer 7

The top 2% are accepted into the society, i.e. the 2% of the total test scores to the *right* of \(k\). The table of \(z\)-values gives us the proportion of the population that scores to the *left* of \(k\). So if 2% is on the right, how much is on the left?

Answer 8

oh I understand that now, so the answer would be no less than 130?

Answer 9

Right, the minimum score would be 130.

Answer 10

walk me through this one? Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Approximately what percent of pizzas are delivered between 24 and 30 minutes?

Answer 11

Now you want to find \(P(24\le Y\le 30)\), where \(Y\) denotes the delivery time.

Like with the last one, you transform to the \(Z\) distribution:
\[P(24\le Y\le30)=P\left(24\le 3Z+27\le30\right)=P(-1\le Z\le1)=P(1)-P(-1).\]

Answer 12

The link I provided only gives the probabilities for positive \(z\)'s, so here's one that includes negatives: http://dsearls.org/courses/M120Concepts/ClassNotes/Statistics/520A_LeftTailTable.htm

You understand how to find the probabilities, right?

Answer 13

what value comes from that work above?

Answer 14

This is correct!! (Just took the test!) XD

Answer 15

(At least the first one is, that is the one that was on my quiz)

Answer 16

It's nice seeing I can help a year after the fact :)