Question 1121049: Find the probability and interpret the results. If convenient, use technology to find the probability. During a certain week the mean price of gasoline was $2.711per gallon. A random sample of 38 gas stations is drawn from this population. What is the probability that the mean price for the sample was between $2.6982 and $2.715 thatweek? Assume σ=$0.041
The probability that the sample mean was between $2.698 and $2.715 is______
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! during a certain week, the mean price of gas was 2.711 per gallon.
a random sample of 38 gas stations is drawn from this population.
what is the probability that the mean price for the sample was between 2.6982 and 2.715 that week.
assume the standard deviation of the population is .041.
the standard error for the distribution of sample means is equal to standard deviation / square root of sample size.
that makes standard error equal to .041 / sqrt(38) = .0066510783
using the following online normal distribution calculator, i get a probability of 0.6991
i also did the problem using z-scores and got a probability of 0.6991 again.
this stands to reason since the z-score formula depends on the raw scores, so if i got .6991 with the raw scores, i should expect to get .6991 with the z-scores.
here's the raw scores display.
here's the z-scores display.
when using raw scores, and when converting raw scores to z-scores, the calculation of the standard error of the distribution of sample means is critical.
get that wrong and the answer comes out wrong.
when you're dealing with the mean of a sample of a certain size, you do not use the standard deviation of the population.
you have to calculate the standard error using the following formula.
standard error = standard deviation of population or of a particular sample divide by the square root of the sample size.
in your problem, you were given the standard deviation of the population at .041.
with a sample size of 38, the standard error was calculated to be .041 / sqrt(38) = .0066510783.
the calculator i used can be found at http://davidmlane.com/hyperstat/z_table.html
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