STAT2001 -Statistics week 3 Assignment.
Do all 6 questions. Show your steps clearly. Deadline for this assignment is 12th Nov. 6:30p.m. You can submit to the assignment locker (next to LSB 125) or to your Tutors. 1. A filling station is supplied with gasoline once a week. If its weekly volume of sales in thousands of gallons is a random variable with probability density function
What should the capacity of the tank to be so that the probability of the supply’s being exhausted in a given week is 0.01?
2. The annual rainfall (in inches) in a certain region is normally distributed with mean = 40, standard deviation = 4. What is the probability that starting with this year, it will take over 10 years before a year occurs having a rainfall of over 50 inches? In your calculation, what additional assumption are you making?
3. The number of years a radio functions is exponentially distributed with parameter θ=8. If Jones buys a used radio, what is the probability that it will be working after an additional 8 years?
4. Let X equal the number of alpha particle emissions of carbon-14 that are counted by a Geiger counter each second. Assume that the distribution of X is Poisson with mean 16. Let W equal the time in seconds before the seventh count is made. Find P(W≤0.5).
5. If 10 observations are taken independently from chi-square distribution with 19 degrees of freedom, find the probability that exactly 2 of the 10 sample items exceed 30.14.
6. If X follows N(µ,σ2), show that
. STAT2001 -Statistics week 3 Assignment