Suppose that engineering specifications on the shelf depth of a certain slug to be turned on a cnc lathe are from .0275 in. to .0278 in. and that values of this dimension produced on the lathe can be described using a normal distribution with mean μ and standard deviation σ . (a) if μ = .0276 and σ = .0001, about what frac- tion of shelf depths are in specifications? (b) what machine precision (as measured by σ ) would be required in order to produce about 98% of shelf depths within engineering spec- ifications (assuming that μ is at the midpoint of the specifications)?

The amount of calories consumed by customers at the chinese buffet is normally distributed with mean 2743 and standard deviation 652. one randomly selected customer is observed to see how many calories x that customer consumes. round all answers to 4 decimal places where possible. a. what is the distribution of x? x ~ n(correct,correct) b. find the probability that the customer consumes less than 2355 calories. incorrect c. what proportion of the customers consume over 3026 calories? incorrect d. the piggy award will given out to the 1% of customers who consume the most calories. what is the fewest number of calories a person must consume to receive the piggy award? incorrect calories. (round to the nearest calorie)