SOLUTION: The mean of a random sample of n=100 is going to be used to estimate mean daily production of a very large herd of dairy cows.Given that the standard deviation of the population sa

Question 1049944: The mean of a random sample of n=100 is going to be used to estimate mean daily production of a very large herd of dairy cows.Given that the standard deviation of the population sampled is 3.6 quarts,what can we assert about probabilities that the error of this estimate will be,
(a)more than 0.72 quarts
(b)less than 0.45 quarts?

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
std dev of sample = std dev of the population/ square root of sample size
:
std dev of sample = 3.6 / square root(100)
:
std dev of sample = 3.6 / 10 = 0.36
:
we use the 68-95-99.7 rule for 1, 2 , 3 standard deviations
:
*******************************************************************************
(a) asks us what is the probability that the error of the estimate for the mean of the sample is greater than 2 standard deviations
:
this will be (99.7 - 95) / 2 = 2.35%
:
note why did I have to divide by 2?
*******************************************************************************
:
******************************************************************************
(b) asks us what is the probability that the error of the estimate for the mean of the sample is less than 0.45
:
0.45 = 0.36 (1 standard deviation) + 0.09 (1/4 of 1 standard deviation)
:
this will be (99.7/2) + (68/2) + (95/(4*2)) = 95.725%
:
******************************************************************************

RELATED QUESTIONS
The mean daily production of a herd of cows is assumed to be normally distributed with a... (answered by ewatrrr)

The mean daily production of a herd of cows is assumed to be normally distributed with a... (answered by math_helper)

The mean daily production of a herd of cows is assumed to be normally distributed with a... (answered by ewatrrr)

A population has a mean of 200 and a standard deviation of 50.suppose a simple random... (answered by Boreal)

A population has a mean of 200 and a standard deviation of 50. Suppose a simple random... (answered by stanbon)

The mean daily production of a herd of cows is assumed to be normally distributed with a... (answered by ikleyn)

9. A population has a mean of 200 and a standard deviation of 50. A simple random sample... (answered by onyulee)

Before the change the average sales used to be 24952$ a day with a standard deviation of (answered by stanbon)

Which of the following statistics are unbiased estimators of population parameters? a.... (answered by edjones)