SOLUTION: In a normal distribution with a mean and a std deviation, how do you find the probability of selecting 3 random units, whose total average exceeds a certain value?
For example,
Algebra.Com
Question 208486: In a normal distribution with a mean and a std deviation, how do you find the probability of selecting 3 random units, whose total average exceeds a certain value?
For example, normal distribution with mean of 127, and SD of 3.1: what is the probability that if three random units are selected, their total average (add up the values and divide by three), is greater than 130?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In a normal distribution with a mean and a std deviation, how do you find the probability of selecting 3 random units, whose total average exceeds a certain value?
For example, normal distribution with mean of 127, and SD of 3.1: what is the probability that if three random units are selected, their total average (add up the values and divide by three), is greater than 130?
-----------------
That average you are referring to is the sample mean.
----
Since the population mean is 127, the mean of the sample means is 127.
Since the SD of the population is 3.1, the SD of the sample means is 3.1/sqrt(3)
----
These facts are known because of the "Central Limit Theorem".
-----------------------
So find the z-value of 130:
z(130) = (130-127)/[3.1/sqrt(3)] = 1.676
---
This tells you that 130 is 1.676 standard deviations to the right of the
mean of the sample means, which is 127.
9
Then P(a sample mean could be greater than 130) = P(z> 1.676) = 0.0469
-------------------------------------------
Cheers,
Stan H.
PS. If you have any response to this email stanbon@comcast.net as the
feedback function of algebra.com is not working.
RELATED QUESTIONS
A standardized IQ test provides a normal distribution of scores with a mean of 100 and a... (answered by ewatrrr)
According to records of commonwealth Edison, the mean electric consumption
during... (answered by psbhowmick)
Assume x has a standard normal distribution and a mean of 45 with a standard deviation of (answered by Fombitz)
Can someone show me how to work these type of math questions? Please, check the ones I... (answered by stanbon)
So we have a normal distribution of test scores. Mean score is 120; std deviation is... (answered by stanbon)
Hi can someone please show me how to do questions like the following involving the normal (answered by rothauserc)
On the midnight shift, the number of patients with head trauma in an emergency room has... (answered by stanbon,jim_thompson5910)
Suppose you have a normal distribution of values with a mean of 70 and a standard... (answered by mathmate)
How do I solve these questions manually (i.e. using the standardised normal distribution... (answered by Theo)