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Juliette [100K]
3 years ago
15

The average electric bill for a small electric company is $72 for the month of April with a standard deviation of $6. If the amo

unts of the bills are normally distributed, find the probability that the mean of the bills for 15 randomly selected residents will be less than $75
Mathematics
1 answer:
SVEN [57.7K]3 years ago
6 0

Answer:

Hence the probability that the mean of their utility bills will be less than $75 = P(X < 75) is 0.9736.

Step-by-step explanation:

Now,  

Population mean electric bill, \mu =  $72  

Population standard deviation, \sigma =  $6  

Standard error of the mean= \sigma / \sqrt{n} = 6 / \sqrt{15} = 1.5492

The probability that the mean of their utility bills will be less than $75 = P(X < 75)

= P[Z < (75 - 72) / 1.5492]

= P[Z < 1.9365]

= 0.9736 (Using Z table)

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