Question

The mean value of land and buildings per acre from a sample of farms is $1200, with a standard deviation of $100.The data set has a​ bell-shaped distribution. Assume the number of farms in the sample is 78.

Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1000 and $1400

Answer 1

answer:

given data ,

$\Rightarrow$ the sample farms is $1200

$\Rightarrow$ the standard deviation is $100

$\Rightarrow$ the assumed farms is 78

to estimation of the number of farms values of the betwens $1000 and $1400.....?

$\Rightarrow$ The experimental guideline expresses that 68% of qualities will be inside 1 standard deviation from the mean, 95% will be inside 2, and 99.7% will be inside three.

$\Rightarrow$ To make sense of this, you should initially make sense of what number of standard deviations every endpoint is from the mean utilizing the recipe: (esteem - mean)/(standard dev.) - this is known as a z-score.

$\Rightarrow$ On the off chance that the z-score is negative, the esteem is underneath the mean; if positive, it is over the mean.

$\Rightarrow$ Somewhere in the range of 1000 and 1400.

$\Rightarrow$ the Discover the z-scores.

$\Rightarrow$ For these 1000: (1000 - 1200)/100 = - 2

$\Rightarrow$ For these  1400: (1400-1200)/100 = +2

$\Rightarrow$ Since qualities inside this range fall inside 2 standard deviations from the mean in either course, 95% of the qualities will fall between this range.

$\Rightarrow$ Since the quantity of ranches in the example is 78, we should now take 95% of 78 in light of the fact that that will give us the quantity of homesteads whose qualities per section of land are somewhere in the range of $1000 and $1400:

$\Rightarrow$ (0.95)(78)

$\Rightarrow$ 75.05

$\Rightarrow$ 74.1 ranches

$\Rightarrow$ there fore 74.1 ranches