16.The waiting time until a subway train arrives follows a uniform distribution where the minimum wait is 0 minutesand the maximum wait is 10 minutesa.Find the probability of waiting less than 3minutes for the next train. .
b.Find the median waiting time.
c.Find the probability of waiting exactly 2minutes for a train.
d.Giventhe passenger has already waited 2 minutes, find the probability of waiting a total of 5 or moreminutes for the train.
17.The age of a grove of walnut trees follow a Normal Distribution with μ=50 years and σ=15 years. a.Find the probability that the age of a randomly selected tree is between 40 and 70 years.
b.Find the probability of a randomly selected tree has lived exactly 45.231789 years.
c.Find the 30thpercentile of this distribution.
18.The amount of a cement in a construction store follows a uniform distribution where the minimum time is 10 tons and the maximum time is 50 tons. For this distribution μ= 30 tons and σ= 14.14. a.Find the probability the wait for a randomly selected passenger is between 25 and 37 minutes.
b.Find the 55thpercentile of this distribution.
c.A random sample of 36 passengers is taken. Find the probability the sample meanexceeds 33 minutes.
19.Accidents occur at an oil refinery on the average once every 3 years. The waiting time until the next accident follows an Exponential Distribution. a.Find the probability of waiting at least 5 years until the accident.
b.Find the Median waiting time until the next accident.
The random variable Y represents the daily car sales at an auto dealership. The population mean is 49 sales per day and the standard deviation is 7 sales per day. The probability distribution shape of Y is Poisson and a sample of 100 days is randomly selected. 7
Distribution is Normal (Three parts of the Central Limit Theorem)