Find the probability that the average price for 30 gas stations is less than $4.55.
I need to verify the steps for this and see if there is another way to do this problem; please help. Include an explanation of what was done.
The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen. We are interested in the average cost of gasoline for the 16 gas stations.
Find the probability that the average price for 30 gas stations is less than $4.55.
a. 0.6554
b. 0.3446
c. 0.0142
d. 0.9858
e. 0
C is the correct answer. P(x<4.55). The Mean is 4.59. The Standard Deviation is 0.10. N = 30 gas stations. To find the Z score I calculated 4.55−4.59(0.1030√)= -2.19. I then calculated the probability using Minitab and got an answer of 0.0142
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