# statistics

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The average electric bill in a residential area is \$72 for the month of May. The standard deviation is \$6. If the amounts of electric bills are normally distributed, find the probability that the mean of the bill for 15 residents will be less thatn \$75

• statistics -

You need to work out the standard deviation of the mean of the bill for 15 residents. That's \$6//sqrt(15), which is 1.549. So the distribution of the mean of the bill for 15 residents will be Normal, with mean \$72 and standard deviation 1.549. You have to work out the probability that the mean will be less than \$75, so you need work out how many standard deviations \$75 is above \$72, which is (\$75 - \$72) divided by \$1.549, which is 1.936. You now need to know what the area to the left of that point (because you want the probability of the mean bill being less that \$75) is, and you can get that from a set of Normal probability tables. If you were looking up 1.96 you would get an answer of 0.975, so you know it's going to be a bit less than that. I've just looked it up myself, and I get 0.9735 - so I reckon that's your answer - i.e. just over 97%.