Question

The mean value of land and buildings per acre from a sample of farms is ​$1300​, 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)? ​$912  ​$1883  ​$1369  ​$580  ​$1593  ​$1582

Which of the farms are unusual​ (more than two standard deviations from the​ mean)? Select all that apply.

A. $1593

B. ​$912

C. ​$1582

D. ​$1369

E. ​$1883

F. ​$580

Which of the farms are very unusual​ (more than three standard deviations from the​ mean)? Select all that apply.

A. ​$1883

B. ​$1593

C. ​$912

D. ​$1582

E. ​$1369

F. ​$580

G. None of the data values are very unusual.

Answer 1

95 % values lies between 2 standard deviation of the mean .

Mean -2 SD, Mean +2SD

1300-2*200, -1300+2*200

(900,1700)

Values E and F seems unusual because they are not lies within (900,1700)

99 % values lies between 3 standard deviation of the mean .

Mean -3 SD, Mean +2SD

1300-3*200, -1300+3*200

(700,1900)

Value F seems unusyy, because it is not lie in (700,1900)