SOLUTION: In a sample of 900 gas​ stations, the mean price for regular gasoline at the pump was $ 2.874 per gallon and the standard deviation was ​$0.009 per gallon. A random sam

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Question 1112003: In a sample of 900 gas​ stations, the mean price for regular gasoline at the pump was $ 2.874 per gallon and the standard deviation was ​$0.009 per gallon. A random sample of size 55 is drawn from this population. What is the probability that the mean price per gallon is less than ​$2.872​?
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
The sample size(55) is greater than 45(1/20 * 900), we use the following formula for the standard error(SE) of the sampling mean
:
SE = (standard deviation/square root(sample size)) * square root((900-55)/(900-1))
:
SE = (0.009/square root(55)) * square root(845/899) = 0.0012
:
since the sample size(55) is > 30 and we know the standard deviation(0.009), we use the normal distribution's z-score and z-score tables
:
z-score = (2.872 - 2.874)/(0.0012) = −1.6667
:
Probability (X < 2.872) = 0.0475
: