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. From the histogram, the relative frequency of houses with a value less than 500,000 is 0.34 and 0.37

-#The probability can therefore be calculated as:

$P(500000)=P(x=0)+P(x=500)\\\\\\\\=0.34+0.37\\\\\\\\=0.71$

Hence, the probability of the house value being less than 500,000 is o.71

b.

-From the info provided, we calculate the mean=403 and the standard deviation is 278 The probability that the mean value of a sample of n=40 is less than 500000 can be calculated as below:

$P(\bar X$

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