Statistics and Probability

Independent Activity 1:

The number of shoes sold per day at retail store is shown in the below.

X: 19 20 21 22 23

P(X): 0.4 0.2 0.2 0.1 0.1

Independent Assessment 1:

Formula to be used:

a. Mean:

• μ = ΣX • P(X)

b. Variance:

• σ²=Σ(X - μ)^² • P(X)

c. Standard Deviation:

Solution:

Multiply value of the random variable x by the corresponding probability:

X • P(X)

Get the mean by getting the sum of X • P(X)

μ = ΣX • P(X)

μ = 7.6 + 4 + 4.2 + 2.2 + 2.3

Subtract the mean from each value of the random variable x:

X - μ

Square the results of X - μ

(X - μ)²

Multiply the results of (X - μ)² by the corresponding probability:

(X - μ)² • P(X)

Get the sum of the results in (X - μ)² • P(X) to get the variance:

Get the square root of the variance to get the standard deviation:

Independent Activity 2

The number of patients seen in the Emergency Poor in any given hour is a

random variable represented by x. The probability distribution for x is:

X: 10 11 12 13 14

P(X): 0.4 0.2 0.2 0.1 0.1

Independent Assessment 2:

Formula to be used:

a. Mean:

• μ = ΣX • P(X)

b. Variance:

• σ²=Σ(X - μ)^² • P(X)

c. Standard Deviation:

Solution:

Multiply value of the random variable x by the corresponding probability:

X • P(X)

Get the mean by getting the sum of X • P(X)

μ = ΣX • P(X)

μ = 4 + 2.2 + 2.4 + 1.3 + 1.4

Subtract the mean from each value of the random variable x:

X - μ

Square the results of X - μ

(X - μ)²

Multiply the results of (X - μ)² by the corresponding probability:

(X - μ)² • P(X)

tex]14 • 7.29 = 102.06[/tex]

Get the sum of the results in (X - μ)² • P(X) to get the variance:

Get the square root of the variance to get the standard deviation:

Independent Activity 3:

X: 0 1 2 3 4

P(X): 1/16 1/4 3/8 1/4 1/16

Independent Assessment 3:

Formula to be used:

a. Mean:

• μ = ΣX • P(X)

b. Variance:

• σ²=Σ(X - μ)^² • P(X)

c. Standard Deviation:

Solution:

Multiply value of the random variable x by the corresponding probability:

X • P(X)

Get the mean by getting the sum of X • P(X)

μ = ΣX • P(X)

μ = 0 + 0.25 + 0.75 + 0.75 + 0.25

Subtract the mean from each value of the random variable x:

X - μ

Square the results of X - μ

(X - μ)²

Multiply the results of (X - μ)² by the corresponding probability:

(X - μ)² • P(X)

tex]4 • 4 = 16[/tex]

Get the sum of the results in (X - μ)² • P(X) to get the variance:

Get the square root of the variance to get the standard deviation:

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