1.) In a National Highway Traffic Safety Administration report, data provided to the NHTSA by Goodyear stated that the average tread life of property inflated automobile tires is 45,000 miles. Suppose that the current distribution of tread life of properly inflated automobile tires is normally distributed with a mean with a mean of 45,000 mies and a standard deviation of 2360 miles.

a.) Suppose that 6% of all automobile tires with the longest tread life have a tread life of at least x miles. Find the value of x.

b.) Suppose that 2% of all automobile tires with the longest tread life have a tread life of at least x miles. Find the value of x.

2.) Spoke Weaving Corportion has eight weaving machines of the same kind and of the same age. The probability is 0.04 that any weaving machine will break down at any time. Find the probability that an any given time :

a.) all eight weaving machines will be broken down.

b.) exactly two weaving machines will be broken down.

3.) Paige Darby, who lives in the San Francisco Bay area, commutes by the car from home to work. She knows that it takes her an average of 28 minutes for this commute in the morning. However, due to the variability in the traffic situation every morning, that standard deviation of these commutes is 5 minutes.  Suppose the population of her morning commute times has a normal distribution with a mean of 28 minutes and a standard deviation of 5 minutes. Paige has to be at work by 8:30 am every morning. By what time must she leave home in the morning so that she is late for work at most 1% of the time?