The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is as follows: Houses Sold (x) Probability P(x)
0 0.24
1 0.01
2 0.12
3 0.16
4 0.01
5 0.14
6 0.11
7 0.21
Find the mean of the given probability distribution.
A. μ = 3.35
B. μ = 3.50
C. μ = 3.60
D. μ = 3.40

C. μ = 3.60

Step-by-step explanation:

Two tables have been attached to this response.

One of the tables contains the given data and distribution with two columns: Houses Sold and Probability

The other table contains the analysis of the data with additional columns: Frequency and Fx

=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,

When the number of houses sold = 0

F = P(0) x Total number of houses sold

F = 0.24 x 28 = 6.72

When the number of houses sold = 1

F = P(1) x Total number of houses sold

F = 0.01 x 28 = 0.28

=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,

When the number of houses sold = 0

Fx = F * x

F = 6.72 x 0 = 0

Now to get the mean, μ we use the relation;

μ = ∑Fx / ∑F

Where;

∑Fx = summation of the items in the Fx column = 100.8

∑F = summation of the items in the Frequency column = 28

μ = 100.8 / 28

μ = 3.60

Therefore, the mean of the given probability distribution is 3.60

step-by-step explanation:

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