Can someone please help me solve this question set? Thank you

[Netflix] In 2019, 2.7 million Americans still get Netflix DVDs in the mail. 1 Key reasons include that streaming offers a limited selection compared with DVDs, and rural America struggles with broadband access, etc. One of the key decisions at Netflix DVD is to determine how many copies of newly released titles each regional warehouse should purchase. When making inventory decisions, one factor Netflix needs to be concerned with is the variability of rent cycle time (from the time that a DVD is placed in a mail until the time that it is returned, processed, and ready to be shipped again). In an ideal world where the rent cycle time is perfectly predictable and is the same for every customer, Netflix can easily figure out how many copies it needs to stock. However, in reality, some customers turn around the DVDs fast while others hold onto them for weeks. This variability is the reason that Netflix becomes interested in tracking the total rent cycle time and utilize the information in their stocking decision. (FYI, Netflix also utilizes a tactic to buy some time by sending a DVD from the customer's queue instead of making them wait for a specific DVD.) The total rent cycle time can be decomposed in four components: Total rent cycle time (T) = Home Delivery Time (H)+ Time that a DVD stays with a customer (D) + Return Delivery Time (R)+ Return processing and restocking time (S) =H+D+R+S After several rounds of lean implementation and process innovation, Netflix can process the return and restock in 1 day with certainty (S=1). On the other hand, delivery times (both from and to the Warehouse)- H and R-are random and so is the time that a DVD stays with a customer (D). After looking at the histograms of past transactions, the one-way delivery time (both home and return deliveries) seems to approximately follow a normal distribution with mean of 1.5 days and standard deviation of 0.5 days. A further study shows that home delivery time and return delivery time are independent. Historical data also shows that for most new releases, the time that a DVD stays with a customer (D) is normally distributed with mean 7 of days and standard deviation of 2.5 days. For the purpose of analysis, you can assume that Netflix and the Postal Service work 24 hours a day and 7 days a week (so that you do not have to round each number). Also, for the purpose of your analysis, you can assume that all of four time components are independent of each other. 22. [2 pts] Recall that home delivery time is approximately normally distributed with mean of 1.5 days and standard deviation of 0.5 days. What is the probability that a home delivery takes two or fewer days? 23. [2 pts] If Netflix randomly samples 10 home deliveries, what is the probability that 7 or fewer deliveries take two or fewer days? 24. [2 pts] Find the mean and standard deviation of the round-trip delivery times (H+R). If home delivery and return delivery times follow normal distributions, what distribution does the round trip delivery time (H+R) follow? What are the mean and standard deviation of the round-trip delivery time (H+R) ? 25. [2 pts] A manager at the warehouse argues that the standard deviation of the round trip delivery time should be 20.5=1 day. Is his argument correct? Please provide a brief explanation ( 1 or 2 sentences) to discuss whether his argument is right or wrong. 26. [2 pts] Based on the information, describe the distribution of the total rent cycle time. Please specify the distribution, mean, and standard deviation. Distribution: Why: Mean: Standard deviation: 27. [3 pts] Netflix is concerned that some subscribers holding on to new releases too long. Netflix wants to send a reminder to 10% of its subscribers who still hold new DVDs too long before they send back. Netflix believes that such a reminder will speed up circulation of new DVDs and will enable Netflix to provide the same level of service with fewer copies. How many days should Netflix wait (from the time at which the DVD is mailed from the warehouse) before sending out the reminder? Hint: Netflix wants to send messages to customers who still have the DVDs at their home. Should you use the total rent cycle time (H+D+R+S) or a portion of the total rent cycle time when measuring the time until they mail back