Can you solve these problem with out use integral can you to convert to normal standart diviation which one needed as well as use z table.

thank you

1. According to Consumer Response Annual Report, millennials spent an average of $103 on monthly dining in 2016. Let the amount spent on a monthly dining be normally distributed with unknown standard deviation. Assume that the probability of a randomly-selected millennial that spends more than $133 is 10%, and the probability that a randomly-selected millennial that spends less than $97 pounds is 40%. What is the probability that a randomly-selected millennial will spend between $73 and $109 on a monthly dining? (Solve problem by using your hand calculation and R).

2. The scheduled commuting time on the Long Island Railroad from Glen Cove to New York City is 65 minutes. Suppose that the actual commuting time is uniformly distributed between 64 and 74 minutes. (Solve problem by using your hand calculation and R).

(a) What is the probability that the commuting time will be less than 70 minutes?

(b) What is the probability that the commuting time will be between 65 and 70 minutes?

(c) What are the expected commuting time and the standard deviation of the commuting time?

(d) How much can the expected commuting time be decreased if the actual commuting time is distributed between 60 and 74?

3. Suppose that 10% of the probability for a normal distribution with mean and standard deviation is below 50 and that 5% is above 80. What are the values of and . (Solve problem by using your hand calculation and R).

4. Suppose that X is the downloading time a movie, which follows a uniform distribution between 16 and 22 minutes. Let's assume you want to download a movie. What is the probability that the download time will be

a. Less than 19 minutes?

b. More than 23 minutes?

c. Between 20 and 22 minutes?

d. What are the mean and standard deviation of the download times? (Solve problem by using your hand calculation and R).

5. The speed at which you can log into a website through a smartphone is an important quality characteristic of that website. In a recent test, the mean time to log into the JetBlue Airways website through a smartphone was 4.237 seconds. (Data extracted from N. Trejos, "Travelers Have No Patience for Slow Mobile Sites," USA Today, April 4, 2012, p. 3B.) Suppose that the download time is normally distributed, with a standard deviation of 1.3 seconds. What is the probability that a download time is

a) Less than 2 seconds?

b) Between 1.5 and 2.5 seconds?

c) Above 1.8 seconds

d) Ninety-nine percent of the download times are slower (higher) than how many seconds?

e) Ninety-five percent of the download times are between what two values, symmetrically distributed around the mean.

(solve this problem by your hand and r)