A shopping mall estimates the probability distribution of the number of stores m

Question

A shopping mall estimates the probability distribution of the number of stores mall customers actually enter (x), as shown in the table below:

x

P (x)

0

.05

1

.13

2

.22

3

.28

4

.12

5

?

6

.16                                                       Calculate the mean. Calculate the variance and standard deviation of this distribution. Show your work.

x

P (x)

0

.05

1

.13

2

.22

3

.28

4

.12

5

?

6

.16                                                       Calculate the mean. Calculate the variance and standard deviation of this distribution. Show your work.

Explanation / Answer

P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

or, 0.05 + 0.13 + 0.22 + 0.28 + 0.12 + P(5) + 0.16 = 1

or, P(5) = 1 - 0.96

or, P(5) = 0.04

Mean, E(x) = 0 * 0.05 + 1 * 0.13 + 2 * 0.22 + 3 * 0.28 + 4 * 0.12 + 5 * 0.04 +6 * 0.16

                  = 3.05

E(X2) = 02 * 0.05 + 12 * 0.13 + 22 * 0.22 + 32 * 0.28 + 42 * 0.12 + 52 * 0.04 +62 * 0.16

        = 12.21

Var(X) = E(X2) - (E(X))2

           = 12.21 - 3.052

           = 2.9075

Standard deviation = sqrt(2.9075) = 1.7051

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.