Question

The mean value of land and buildings per acre from a sample of farms is ​$1400​, with a standard deviation of ​$200. The data set has a​ bell-shaped distribution. Using the empirical​ rule, determine which of the following​ farms, whose land and building values per acre are​ given, are unusual​ (more than two standard deviations from the​ mean). Are any of the data values very unusual​ (more than three standard deviations from the​ mean)?

​$1619  ​$1881  ​$1163  ​$658  ​$1118  ​$1122

Answer 1

given -

Mean = $1400​

standard deviation = ​$200

also distribution is bell curve shape.

now

land and building values per acre are​ given which are unusual​ =

values more than two standard deviations from the​ mean

= [mean - 2 * S.D , mean + 2 * S.D]

= [1400 - 2 *200 , 1400 + 2* 200]

= [ 1000 , 1800]

values which are below 1000 or above 1800 will be considered as unusual.

​$1881 ,$658 are unusual.

now very unusual =

values more than three standard deviations from the​ mean =

[mean - 3*SD , mean + 3 * SD]

= [1400 - 3 * 200 , 1400 + 3 * 200]

= [ 800 , 2000]

values below 800 and above 2000 are considered very unusual.

658 is very unusual.

please like)