Question

The mean value of land and buildings per acre from a sample of farms is ​$1500​, with a standard deviation of ​$100. The data set has a​ bell-shaped distribution. Assume the number of farms in the sample is 78.

​(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between ​$1300 and ​$1700.

___farms

Answer 1

(A) given that

mean = 1500

standard deviation (sd) = 100

and n = 78

we have to estimate the number of farms whose land and building values per acre are between ​$1300 and ​$1700.

we can write 1300 as 1500 - 2*100, i.e. it is 2 standard deviation below the mean

and we can write 1700 as 1500 + 2*100, i.e. it is 2 standard deviation above the mean

using empirical rule,we know thaty 95% of data is between 2 standard deviations from the mean

So, required number of farms = n*p

= 78*0.95

= 74.1

= 75 (rounded to next integer)