Question

The length of college football games is normally distributed with a mean time of 210 minutes and a standard deviation of 30 minutes.
A random sample of 64 games is taken and 20 of them are longer than 230 minutes.
Find the sample proportion and describe the distribution of sampling proportion.

Answer 1

@kropot72

Answer 2

Please wait a while for my help. I'm just about to eat :)

Answer 3

lol okay

Answer 4

For the first step, I think the probability of a game taking longer than 230 minutes should be found from the given values of the mean and standard deviation for the population.
Are you able to do that?

Answer 5

Do you mean convert the sample proportion to the z-score,

Answer 6

I know the sample proportion=20/64 which equals .31

Answer 7

Not really. Just get the z-score for 230 minutes, and find the probability that a game lasts longer than 230 minutes. This is a first step.

Answer 8

But the question says find the sample proportion. It does not say anything about finding the z-score.

Answer 9

also the standard deviation for the sample proportion is

Answer 10

What should I plug for P, because actually I was thinking that p was the proportion of the population mean

Answer 11

Yes, the sample proportion with a time longer than 230 minutes is 0.3125. However we can find the proportion of the population with a time longer than 230 using the given values of the mean and standard deviation for the population. You also need to describe the distribution of the sampling proportion. The standard error of the sample proportion is given by:
\[\large \sqrt{\frac{p(1-p)}{n}}\]
where n is the sample size and p is the proportion of the sample with a time longer than 230.
As for the type of distribution of the sample proportion, this can be found from the Central Limit Theorem where the sample size > 30.

Answer 12

so in the sample proportion of standard deviation, p will equal s 0.3125 or 210

Answer 13

The standard error of the sample proportion
\[\large \sqrt{\frac{p(1-p)}{n}}\]
is used for the standard deviation of P.
Use 0.3125 for the value of p in your calculation.

Answer 14

Ok thanks bro, I was confused because I thought that we use the mean for p

Answer 15

Using the given parameters for the population, the the proportion of the population with a time longer than 230 (represented by pi) is given by:
\[\large \pi=0.2514\]
We already found that the proportion of the sample with a time longer than 230 is:
\[\large p=0.3125\]
When you have found the value of the standard deviation of the sampling proportion of games lasting longer than 230 minutes, you can find how many standard deviations (of the sampling distribution) below p is pi.