Suppose that the lifetimes of light bulbs are approximately normally​ distributed, with a mean of 57 hours and a standard deviation of 3.5 hours. With this​ information, answer the following questions.   ​(a) What proportion of light bulbs will last more than 62 ​hours? ​(b) What proportion of light bulbs will last 52 hours or​ less? ​(c) What proportion of light bulbs will last between 59 and 62 ​hours? ​(d) What is the probability that a randomly selected light bulb lasts less than 45 ​hours?

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Q: The monthly utility bills in a city are normally​ distributed, with a mean of $100 and a standard…

A:

Q: The monthly utility bills in a city are normally​ distributed, with a mean of ​$100 and a standard…

A:

Q: e monthly utility bills in a city are normally​ distributed, with a mean of ​$100   and a standard…

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Q: he monthly utility bills in a city are normally​ distributed, with a mean of $100 and a standard…

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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!