Please provide a thorough explanation for study purposes.

1.

(10 points) An amazon delivery driver always seems to be going to the same house first after being loaded down with packages at the local distribution center. The delivery driver got curious about their delivery time from the distribution center to the first house on the route and found that their delivery time is normally distributed with a mean value of 8.46 minutes and a standard deviation of .913 minutes. (a) What is the probability that it will take the delivery driver at most 10 minutes to make the first delivery? (2 points) (b) What is the probability that it will take the delivery driver longer than 15 minutes to make the first delivery? (2 points) (c) What is the probability that it will take the delivery driver between 8 and 10 minutes to make the first delivery? (2 points) (d) What value of c is such that 98% of all first house delivery times are in the interval from 8.46 - c to 8.46 + c? (2 points) (e) If four first house delivery times are independently selected, what is the probability that at least one of them exceeds 10 minutes? (2 points)