The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance is as follows. Payment (Damage Claim Paid) $0 $500 $1,000 $3,000 $4,000 $8,000 $19,000 Probability .85 .04 .04 .03 .02 .01 .01 What is the standard deviation of the claims paid? Give your answer as an integer (0 decimal places). The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 68 miles per gallon and a standard deviation of 9 miles per gallon. What is the probability that, if driven normally, the car will get between 92 and 100 miles per gallon? Give your answer to 4 decimal places. A sample of 37 AA batteries had a mean lifetime of 555 hours and a standard deviation of 13.79 hours. What is the right-hand side of a 95% confidence interval for the mean battery life in the population? Give your answer to 2 decimal places. A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes in a day is normally distributed with a mean of 10,807 and a standard deviation of 1,141 steps. What proportion of the days does he exceed 13,511 steps (i.e., what is the probability he takes more than 13,511 steps)? Give your answer to 4 decimal places.