Question

(a) Suppose one house from the city will be selected at random. Use the histogram to estimate the probability that the selected house is valued at less than $500,000. Show your work.
(b) Suppose a random sample of 40 houses are selected from the city. Estimate the probability that the mean value of the 40 houses is less than $500,000. Show your work.

Answer 1

Answer:

a.   0.71

b.   0.9863

Step-by-step explanation:

a. The mean of the distribution is given as $403,000 and the standard deviation is $278,000.

-To estimate the probability that a randomly selected house  has a value less than $500,000:

$P(X$

Thus, the probability that a randomly selected house has a value less than $500,000 is 0.71

b. -since 40 is larger than or equal to 30, we assume normal distribution.

-The probability can therefore be calculated as:

$P(\bar X)=P(z$

Hence, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863