The daily use of electricity (measured in megawatt-hours) in a certain town is a normal random variable with a mean of 18 and a standard deviation of 6. What is the probability that on a given day, the use of electricity will be between 15.6 and 19.5 megawatt-hours?
Refer to the information in Problem 1.
When the daily use of electricity exceeds the capacity of the power plant, a blackout occurs.
If we know that the probability of a blackout is 0.33, what is the capacity of the power plant?
The daily use of electricity (measured in megawatt-hours) in a certain town is a normal random...
6. In a certain city, the daily consurmption of electric power, in millions of kilowatt-hours, can be treated as a random variable having a gamma distribution with o-3 and 0 -3. If the power plant has a daily capacity of 12 million kilowatt-hours, what is the probability that this power supply will be inadequate on any given day? Scanned with CamScanner
Example 7 The amount of electricity (in hundreds of kilowatt-hours) that a certain power company is able to sell in a day is found to be a random variable with the following probability density function (pdf): kx k(10-x): 0: 0sxs5 5 x 10 elsewhere n) = (i) (ii) Find the value of k. What is the probability that the amount of electricity that will be sold is more than 600 kilowatt-hours. (ii) What is the probability that the amount of...
In a certain city, the daily consumption of electric power in millions of kilowatt-hours, is a random variable X having a gamma distribution with mean p = 15 and variance of = 75. (a) Find the values of a and B. (b) Find the probability that on any given day the daily power consumption will exceed 15 million kilowatt-hours. (a) a= 3 B = 5 (b) The probability is (Round to four decimal places as needed.)
. Metropolitan Power and Light (MPL) tracks peak power usage, measured in gigawatts (GW), for its service area. MPL reports that in January peak daily demand for electrical power follows a normal distribution, with a mean of 4.3 GW and a standard deviation of .8 GW. (Note: A gigawatt is 1 billion watts of electricity, approximately the output of a nuclear fission reactor.) For a randomly selected January day: a. There is a 30% probability that peak demand for electrical...
Advanced Statistics.
1. Assume that the daily profits X of a certain company has a normal distribution with unknown mean μ and standard deviation σ 8 and that we wish to test the Ho 10 against Hi:H< 10 (a) Suppose the the profits over a random sample of n 64 days will be observed Analyst A will reject Ho if the mean daily profits satisfies T <9; hypotheses by two analysts Analyst B will reject Ho if the mean daily...
can u please answer these questions as soon as possible?
Given that z is a standard normal random variable, find z for each situation (to 2 decimals). a. The area to the right of z is 0.03. b. The area to the right of z is 0.045 1.70 C. The area to the right of z is 0.05. 1.64 d. The area to the right of z is 0.1 Television viewing reached a new high when the global information and...
1. The random variable x has a normal distribution with standard deviation 23. It is known that the probability that x exceeds 151 is .90. Find the mean muμ of the probability distribution. 2. In an assessment of the quality of the electrical power system, one measure of quality is the degree to which voltage fluctuations cause light flicker in the system. The perception of light flicker x when the system is set at 380kV was measured periodically (over 10-minute...
the following questions are either true or false answers 1. The Central Limit Theorem allows one to use the Normal Distribution for both normally and non-normally distributed populations. 2. A random sample of 25 observations yields a mean of 106 and a standard deviation of 12. Find the probability that the sample mean exceeds 110. The probability of exceeding 110 is 0.9525. 3. Suppose the average time spent driving for drivers age 20-to-24 is 25 minutes and you randomly select...
1. Suppose that random variables X and Y are independent and have the following properties: E(X) = 5, Var(X) = 2, E(Y ) = −2, E(Y 2) = 7. Compute the following. (a) E(X + Y ). (b) Var(2X − 3Y ) (c) E(X2 + 5) (d) The standard deviation of Y . 2. Consider the following data set: �x = {90, 88, 93, 87, 85, 95, 92} (a) Compute x¯. (b) Compute the standard deviation of this set. 3....
Assume a normal distribution and use a hypothesis test to test the given claim According to city reports, it was found that the mean age of the prison population in the city was 26 years. He obtains a random samplo of 25 prisoners and finds a mean age of 24.4 years and a standard 20. years. Marc wants to test the claim that the mean age of the prison population in his city is less than 26 deviation of 9.2...