Example of Sampling Distribution of the Mean

Statistics: A sample of 169 fish is randomly selected from a large fish population. Fish length X is distributed with a mean of 50 cm and a standard deviation of 26 cm. Find the probability that the sample's mean is between 46 and 48 cm.

[Rumasila]

Omg... After watching idk how many videos, urs has finally helped me find my answer!!! Gahhh, thank u so much! Its 3 am and I have an exam at 10am, so thank you for the simple and quick video!!!

[MathDoctorBob]

A normal distribution is a specific type of distribution.

Sampling distribution of the mean: we have a large population and we wish to measure some quantity for each individual. We do this by sampling - we repeatedly draw samples of size n and take the average/mean. The mean values give a new distribution - the sampling distribution of the mean. In general this won't be normal, but as n gets large, it approximates a normal distribution.

[MathDoctorBob]

@noetherianring Thanks for the comment and support! This run came from helping students, so nothing too fancy. At some point I'll rotate in some actuarial exam preparation.

[MissWooHoo]

this guy looks like a body building bouncer not a Statistician.

[imranali-iywk]

How to make samples in case of without replacement with size 4 can you know any trick please tell me

[vaniedangel]

What is the difference between the sampling distribution of the mean and normal distribution?

[MathDoctorBob]

if we have a large population, it's often impossible to measure every single element to find the true mean. So we approximate using samples (say of fixed size n). If we record the mean for a large number of samples, we get a distribution for the sample mean. This should represent the true mean, but we also want the variance of this distribution. If given the true population variance, divide by n. If this is not known, we approximate using sample variance for true variance.

[latesq]

If the way to get a sample that is representative of a population is to draw the random sample, why do we need to be concerned with sampling error?

[futbolplayercr]

When do we use sigma^2/n as the sample variance and then have the sqrt of that give us the sample standard deviation?

[AlaaMohamed-ctjt]

why the sigma is divided by square root of n ?!

[MathDoctorBob]

This video assumes you know how to use a normal distribution. Once you find mean and standard deviation, you convert to a standard normal distribution using (x-mean)/sd for each term in the inequality; that's where -2 and -1 come from. Then you look these values up in a table.

[shawnl]

Holy shit yeesss, you 5 min video taught better than my prof's 20 min video. Thanks a ton

[Lujo]

Much thanks! Helped me study for my exam.

[MathDoctorBob]

@BooskNetwork You're welcome and good luck! - Bob

[ouroborosnagyok]

Thanks you sir, this was very helpful

[algeddani]

thanxs sir know i have a different why to solve this formela