SOLUTION: If you solve the question below, I'll be appreciated. The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean 0.9 grams per mile and standar

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Question 1205518: If you solve the question below, I'll be appreciated.
The level of nitrogen oxides (NOX) in the exhaust of a particular car model varies with mean 0.9 grams per mile and standard deviation 0.2 grams per mile .
(a) What sample size is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile ?
ANSWER: ?
(b) If a smaller sample is considered, the standard deviation for \bar x would be ? . (NOTE: Enter ''SMALLER'',''LARGER'' or ''THE SAME'' without the quotes.)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Using the formula for the standard deviation of a sampling distribution,
desired standard error=sigma%2Fsqrt%28n+%29
standard error = standard deviation of sampling distribution s
s=sigma%2Fsqrt%28n+%29
where sigma is the population standard deviation, and n is sample size

given that mean is mu=+0.9, standard deviation sigma=0.2, s=0.01, and we need to find

(a) What sample size is needed so that the standard deviation of the sampling distribution is 0.01 grams per mile ?

s=sigma%2Fsqrt%28n+%29
0.01=0.2%2Fsqrt%28n+%29
n+=+%280.2+%2F+0.01%29%5E2+
n=+400
so, you would need a sample size of 400 to ensure the standard deviation of the sampling distribution is 0.01 grams per mile

(b) If a smaller sample is considered, the standard deviation for x_bar would be ?
x_bar=sigma%2F%28n%5E0.5%29
x_bar=0.2%2F%28400%5E0.5%29
x_bar=0.01 => THE SAME