Can someone solve this question? (all the parts correctly and explain pls) An el
ID: 3231264 • Letter: C
Question
Can someone solve this question? (all the parts correctly and explain pls)
An electric utility has placed special meters on 10 houses in a subdivision that measures the energy consumed (demand) in an hour. The company believes that the true population mean is 20 kW. What is the probability that average energy consumed in an hour from this sample of houses is less than 19.5 kW? Define the random variable in words. Is the random variable discrete or continuous? How can you tell? Does the random variable have a specific probability distribution with a name? If so, what is it? What are the numerical values of necessary parameters? What is/are the relevant equations or calculator functions needed to solve this problem? If not, what will have to be derived in order to solve the problem?Explanation / Answer
(a) Deifne the random variable?
The random variable here is the energy consumed in an hour in a house.
(b) Random variable here is continous as it can be any possible value. Not some discrete value.
(c) Yes, random variable have a " Student's t - distribution".
student's t-distribution is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.
Necesaary parameters are mean of the sample = 20 MW
Number of samples = 10
standard deviation of the sample = unknown
Here Pr(xbar <= 19.5; 20 ; s/sqrt(10) by normal distribution calculator.
standard deviation of the population must be derived to solve this problem.