Question

section 16 probability distributions and expected values activity

Section 16 Probability Distributions and Expected Values Activity 2 The following are probability distributions for variable x. Answer the given questions for each: 1. Z less than 4.W {(x) 0.1 0.1 0.2 02 20 a) P(x = 9) b) P(x = 20) c) P( x3) d) The mean for variable x e) The Standard deviation for variable x 120

Answer 1

Solution:

1. We have to find the P(x=20)

We know that the sum of probabilities is 1. Therefore, we have:

$\sum P(x)=1$

$\large 0.1+0.3+0.1+0.2+0.2+P(x=20)=1$

$\large P(x=20)=1-0.9$

$\large P(x=20)=0.1$

a.

$\large P(x \leq 9)=P(x=2)+P(x=3)+P(x=9)$

  $\large =0.1+0.3+0.1$

$\large =0.5$

b.

$\large P(x=20)=0.1$

c.

$\boldsymbol{P(x \geq 3)=P(x=3)+P(x=9)+P(x=11)+P(x=12)+P(x=20)}$

  $=0.3+0.1+0.2+0.2+0.1$

  $=0.9$

d.

The mean of the random variable x is:

$Mean= \sum xP(x)$

  $\boldsymbol{=(2 \times 0.1)+(3 \times 0.3)+(9 \times 0.1)+(11 \times 0.2)+(12 \times 0.2)+(20 \times 0.1)}$

$=0.2+0.9+0.9+2.2+2.4+2$

$=8.6$

e.

The standard deviation for the random variable x is:

$Standard-deviation =\sqrt{\sum P(x)(x-mean)^{2}}$

XP(x) 0.2 0.9 P(x) 0.1 0.3 0.1 0.2 0.2 0.9 2.2 2.4 P(x)(x-mean) 4.356 9.408 0.016 1.152 2.312 12.996 P(x)(x-mean) = 30.24 xP(x) = 8.6 Standard deviation = 30.24 = 5.499