Question

The mean value of land and buildings per acre from a sample of farms is ​$1300​, with a standard deviation of ​$100. 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)?

$1625 $1776 $1585 $1110 $1486 $1673

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

a 1585
b. 1625
c. 1486
d. 1776
e. 1110
f. 1673

Answer 1

1) The unusual values for ( more than two standard deviations from the mean)

a. 1585

b. 1625

d. 1776

f. 1673

2) Are any of the data values very unusual (more than three standard deviations from the mean)?

b. 1625

d. 1776

f. 1673

Explanation:

The Empirical rule formula =

68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

1) We are given the following values,

mean = ​$1300​

standard deviation = ​$100.

We are given data values: $1625 $1776 $1585 $1110 $1486 $1673

We are to find which farms are unusual( more than two standard deviations from the mean)?

Two standard deviation from the mean is between μ – 2σ and μ + 2σ

μ – 2σ

$1300 - 2(100)

= $1300 - 200

= $1100

μ + 2σ

= $1300 + 2 × 100

=$ 1300 + 200

=$ 1500

The values that would be unusual are values that fall bellow 1100 and above 1500

The unusual values ( more than two standard deviations from the mean)?

a. 1585

b. 1625

d. 1776

f. 1673

2) Are any of the data values very unusual​ (more than three standard deviations from the​ mean)?

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

Thres standard deviation from the mean is between μ – 3σ and μ + 3σ

μ – 3σ

$1300 - 3(100)

= $1300 - 300

= $1000

μ + 3σ

= $1300 + 3 × 100

=$ 1300 + 300

=$ 1600

Therefore, the very unusual (more than three standard deviations from the mean)(data that is below 1000 and about 1600) :

b. 1625

d. 1776

f. 1673