Answer:
a) 0.71
b) 0.9863
Step-by-step explanation:
a. Given the mean prices of a house is $403,000 and the standard deviation is $278,000
-The probability the probability that the selected house is valued at less than $500,000 is obtained by summing the frequencies of prices below $500,000:
[tex]P(X<500,000)=P(X=0)+P(X=500)\\\\=0.34+0.37\\\\=0.71[/tex]
Hence, the probability of a house price below $500,000 is 0.71
b. -Let X be the mean price of a randomly selected house.
-Since the sample size 40 is greater than 30, we assume normal distribution.
-The probability can therefore be calculated as follows:
[tex]P(X<x)=P(z<\frac{\bar X-\mu}{\sigma/\sqrt{n}})\\\\P(X<500,000)=P(z<\frac{500-403}{278/\sqrt{40}})\\\\=P(z<2.2068)\\\\\\=0.9863[/tex]
Thus, the probability that the mean value of the 40 houses is less than $500,000 is 0.9863
