To find the probability that the monthly mortgage paid by a randomly selected homeowner from this city is between 3300 and 3800, we need to standardize the values using the z-score formula and then find the area under the normal curve.
First, we determine the z-score for the lower value of 3300:
z1 = (3300 - 2760) / 460 = 1.1739
Next, we determine the z-score for the upper value of 3800:
z2 = (3800 - 2760) / 460 = 2.2609
Using a standard normal distribution table or a calculator, we find the cumulative probability associated with each z-score:
P(z1 < Z < z2) = P(1.1739 < Z < 2.2609) = 0.8647 – 0.8790 = -0.0143
Since the area under the curve cannot be negative, we take the absolute value of -0.0143:
P(3300 < X < 3800) = | -0.0143 | = 0.0143
Therefore, the probability that the monthly mortgage paid by a randomly selected homeowner from this city is between 3300 and 3800 is approximately 0.0143.
the average monthly mortgage payment for all homeowners in a city is 2760. suppose that the distribution of monthly mortgages paid by homeowners in this city follow an approximately normal distribution with a mean of 2760 and a standard deviation of 460. find to 4 decimal places that the probability that the monthly mortgage paid by a randomly selected homeowner from this city is between 3300 and 3800
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