Manny is a realtor and earns 3% commission on the sale of a house. If the house sells for $155,000, how much commission would he
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Answer:
And we can use the following z score:
And replacing we got using the normal standard distribution table or excel:
C.0.8413
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the records of a population, and for this case we know the distribution for X is given by:
Where and
Since the distribution for X is normal then we know that the distribution for the sample mean is given by:
We select a sample of size n=36, and we want to calculate this probability:
And we can use the following z score:
And replacing we got using the normal standard distribution table or excel:
C.0.8413