You survey 1000 new home buyers and find that the mean price was $185,000 and the standard deviation was $20,000. How many paid more than $210,000?
210000 - 185000 = 25000
25000 / 20000 = 1.25 s.d. above the mean
... this is the z-score
use a table to find the fraction above this z-score
To find out how many new home buyers paid more than $210,000, we can use the concept of z-scores. A z-score measures how many standard deviations a particular value is from the mean. We can calculate the z-score for $210,000 using the formula:
z = (x - μ) / σ
Where:
z = z-score
x = value we are interested in ($210,000)
μ = mean ($185,000)
σ = standard deviation ($20,000)
Plugging in the values, we get:
z = (210,000 - 185,000) / 20,000
z = 25,000 / 20,000
z = 1.25
Next, we can use a standard normal distribution table or a calculator to find the proportion of values that have a z-score greater than 1.25. This represents the proportion of home buyers who paid more than $210,000.
Using a standard normal distribution table, we can find that the proportion of values greater than 1.25 is approximately 0.3938.
Finally, to find the actual number of new home buyers who paid more than $210,000, we multiply the proportion by the total sample size:
Number of home buyers = Proportion * Total sample size
Number of home buyers = 0.3938 * 1000
Number of home buyers ≈ 393.8
Therefore, approximately 394 new home buyers paid more than $210,000.