If the weights of coins have too much variation, vending machines will not work correctly. The SRS of the 37 pennies have weights with mean of 2.49g and a standard deviation of 0.016g. U.S. Mint specifications require that the pennies have the mean weight is 2.5g and the standard deviation less than 0.023g. Assume normality and test at the = 0.05 level:

a) the sample comes from a population with mean of 2.5g

the population of weights has a standard deviation less than 0.023g.