Question

The mean value of land and buildings per acre from a sample of farms is

​$1700

with a standard deviation of

​$300

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)?

​$1359

​$2504  

​$1869  

​$609

​$1498

​$2270

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

A.

​$2504

B.

​$1359

C.

​$1498

D.

​$1869

E.

​$609

F.

​$2270

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

A.

​$2270

B.

​$1498

C.

​$609

D.

​$1869

E.

​$2504

F.

​$1359

G.

None of the data values are very unusual.

Click to select your answer(s).

Answer 1

The mean value of land and buildings per acre from a sample of farms is

​$1700

with a standard deviation of

​$300

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)?

​$1359

​$2504

​$1869

​$609

​$1498

​$2270

Answer)

We need to find z score as z score tells us how many s.d away the given score is from the mean

Z = (x - mean)/s.d

Given mean = 1700

S.d = 300

Z for 1359

Z = (1359-1700)/300 = -1.14

Z for 2504

Z = (2504 - 1700)/300 = 2.68

Z for 1869

Z = (1869-1700)/300 = 0.56

Similarly

Z for 609 = -3.64

Z for 1498 = -0.67

Z for 2270 = (2270-1700)/300 = 1.9

A)

Clearly 2504 and 609 are unusual (as z is greater than 2 and less than -2)

B)

Very unusual = 609 as z score is -3.64