Amachine fills 12-ounce bottles with soda. in order for the machine to function properly, the standard deviation of the sample must be less than or equal to 0.03 ounce. a sample of eight bottles is selected and the number of ounces of soda in each bottle is given below. at a=0.05, can we reject the claim that the machine is functioning properly? assume that the variable is normally distributed.12.03 12.10 12.02 11.9812.00 12.05 11.97

Two cyclists 84 miles apart start riding toward each other at the same. one cycles 2 times as fast as the other. if they meet 4 hours later, what is the speed (in mi/h) of the faster cyclist?

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?

3women sell hats at a craft fair weekly. the money they make at the fair is split into categories. 9% goes to pay taxes. $55 goes to pay rent for the space they sell in. the rest is split between the women. if the group make $706 at the fair, how much does each women get paid once the money is divided