V. Money Magazine reported that the average price of gasoline in the United States during the first quarter of 2008 was $3.46. Assume that the price reported by Money is the population mean, and the standard deviation σ is $0.15. a. What is the probability that the mean price for a sample of 30 gas stations is within $0.03 of the population mean?

And we can find this probability using the normal standard table and we got:

Step-by-step explanation:

Let X the random variable that represent the price of a population, and for this case we know the distribution for X is given by:

Where and

And for this case we want to find the following probability:

And we can use the z score formula given by:

If we find the z score for the limits we got:

And we can find this probability using the normal standard table and we got:

b

step-by-step explanation:

t = 3

step-by-step explanation:

put t = 3 in this expression :

(3²-1)(3²-2)(3² - 3)(3² - 4) = 8×7×6×5 = 56×30 = 1680