Assume the price of gas across gas stations in Boston at any particular time has a normal distribution with unknown mean and variance.

In order to estimate the expected price on a given day, you drive to 4 nearby stations and record their prices per gallon as $2.60, $2.90, $2.60 and $2.60.

1. Compute a 95% confidence interval for the expected price for a gallon of gas.

2. Assume now that i tell you that the population standard deviation of gas prices across different stations is known to be 15 cents. How will this information change your 95% confidence interval? Explain.

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