A company claims that the mean monthly residential electricity consumption in a certain region is more than 880 ​kiloWatt-hours (kWh). You want to test this claim. You find that a random sample of 63 residential customers has a mean monthly consumption of 900 kWh. Assume the population standard deviation is 121 kWh. At α=0.05​, can you support the​ claim? Complete parts​ (a) through​ (e). ​(a) Identify H0 and Ha. Choose the correct answer below.     A. H0​: μ=900 Ha​: μ≠900 ​(claim)   B. H0​: μ≤880 Ha​: μ>880 ​(claim)   C. H0​: μ≤900 Ha​: μ>900 ​(claim)   D. H0​: μ>880 ​(claim) Ha​: μ≤880   E. H0​: μ>900 ​(claim) Ha​: μ≤900   F. H0​: μ=880 ​(claim) Ha​: μ≠880 ​(b) Find the critical​ value(s) and identify the rejection​ region(s). Select the correct choice below and fill in the answer box within your choice. Use technology.   ​(Round to two decimal places as​ needed.)   A. The critical value is nothing.   B. The critical values are ±nothing. Identify the rejection​ region(s). Select the correct choice below.     A. The rejection regions are z<−1.64 and z>1.64.   B. The rejection region is z<1.64.   C. The rejection region is z>1.64. ​(c) Find the standardized test statistic. Use technology.   The standardized test statistic is z=nothing. ​(Round to two decimal places as​ needed.) ​(d) Decide whether to reject or fail to reject the null hypothesis.     A. Reject H0 because the standardized test statistic is in the rejection region.   B. Reject H0 because the standardized test statistic is not in the rejection region.   C. Fail to reject H0 because the standardized test statistic is not in the rejection region.   D. Fail to reject H0 because the standardized test statistic is in the rejection region. ​(e) Interpret the decision in the context of the original claim.   At the 5​% significance​ level, there ▼   isis is notis not enough evidence to ▼   support reject the claim that the mean monthly residential electricity consumption in a certain region ▼   is less than is greater than is different from nothing kWh.   Click to select your answer(s).

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!