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:
[tex]P(500000)=P(x=0)+P(x=500)\\\\\\\\=0.34+0.37\\\\\\\\=0.71[/tex]
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:
[tex]P(\bar X<500)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{500-403}{278/\sqrt{40}})\\\\\\=P(z<2.2068)\\\\=0.986336\approx 0.9863[/tex]
Hence, the probability that the mean value of 40 randomly selected houses is less than 500,000 is 0.9863
