n a large city it was found that summer electricity bills for single-family homes followed a normal distribution with a opulation mean μ=500$ and standard deviation of σ=100$. a. What is the probability that randomly chosen single-family home paid less than 370$ bill? (round your answers to 2 decimal places)Answer b. For a random sample of n=400 single-family homes find the probability that more than 100 families paid at least 370$ bills? (hint: P(Y>100)=? Where Y= number of families paid at least 370$ bills and π=P(X≥370))Answer
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!
n a large city it was found that summer electricity bills for single-family homes followed a
a. What is the probability that randomly chosen single-family home paid less than 370$ bill? (round your answers to 2 decimal places)Answer
b. For a random sample of n=400 single-family homes find the probability that more than 100 families paid at least 370$ bills? (hint: P(Y>100)=? Where Y= number of families paid at least 370$ bills and π=P(X≥370))Answer
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