5 your sample of 20 people is being compared to a known...

5. Your sample of 20 people is being compared to a known population with a mean of 100 and a standard deviation of 5. The shape of the distribution is normal. a. The comparison distribution must be a distribution of means. What is the mean of the comparison distribution? b. What is the standard deviation of the comparison distribution (, what is the standard deviation of the distribution of means)? You'll have to first compute the variance of the distribution of means. C. Does the distribution of means have a normal distribution? How do you know?

Transcript

00:01 Hello, svents, we are going to write here your sample of 20 people is being compared to a known population with a mean and standard deviation is given.

00:11 So, she follows normal distribution.

00:13 We are going to find these questions.

00:15 So if i write here for this, what we are given right here, n value as 20, having mean mu value as 100 and standard deviation sigma is standard deviation.

00:36 Deviation sigma value must be written as must be written as 5 if i write here for this this is 5 so now as the shape of the distribution as we know the shape of distribution so let's erase this to make it more clear distribution is normal we are going to have first case what we need to find mean of comparison distribution so for any sample size from a normal population for any sample size any sample or we can write here for sample of any size any size or we can any size drawn from drawn from a normally a normal population we are going to write here for this mu of x is equivalent to mu what does it imply mu of x is equivalent to mu so here here we need to find mean of comparison distribution so mu x is mean of comparison distribution so it means that mu x value must be equivalent to hundred which is mu mean of comparison distribution so now we are going to write here what would be our v part so now standard deviation deviation sigma of x must be sigma divided by n root of n which is sigma value as 5 divided by under root of n and is sample size which is 20 so this value is equivalent to 1 .118 so what is this this value is standard deviation of standard deviation of comparison comparison distribution so now if i write here for this what would we ever see? in the c part we are asked does the distribution of means have a normal distribution how we know that so yes distribution of means have a have a normal distribution we are going to write here as for the sample how we know that? as for the sample of any size, any size drawn.

04:48 This must be, if i write here for this, drawn, drawn from a normally distributed...

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