Q158SE Consider the discrete probabilit... [FREE SOLUTION]

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Statistics For Business And Economics

James T. McClave, P. George Benson, Terry Sincich

$Math Studyset 91影视 Explanations$ Math

13th Edition 路 888 pages

ISBN: 9780134506593

Chapter 8: Q158SE (page 452)

Consider the discrete probability distribution shown here.
x
10
12
18
20
p
.2
.3
.1
.4
a. Calculate $渭, 蟽^{2}$ and $蟽$ .
b. What is $P (x < 15)$ ?
c. Calculate $渭卤 2 蟽$ .
d. What is the probability that xis in the interval $渭卤 2 蟽$ ?

Short Answer

Expert verified

(a) $渭 = 15.4, 蟽^{2} = 18.44 a n d 蟽 = 4.294 .$

(b) $P (x < 15) = 0.5$

(d) The required probability is 0.5.

Step by step solution

Given information

X is a random variable.

Identifying the type of random variable

Mean= $渭$

$渭 = {鈭�}_{i = 1}^{4} x_{j} P (x_{i}) = (10 脳 0.2) + (12 脳 0.3) + (18 脳 0.1) + (20 脳 0.4) = 2 + 3.6 + 1.8 + 8 = 15.4$

Variance= $蟽^{2}$

$蟽^{2} = {鈭�}_{i = 1}^{4} [{(x - 渭)}^{2} P (x)] = ({(10 脳 15.4)}^{2} 脳 0.2) + ({(12 - 15.4)}^{2} 脳 0.3) + ({(18 - 15.4)}^{2} 脳 0.1) + ({(20 - 15.4)}^{2} 脳 0.4) = (29.16 脳 0.2) + (11.56 脳 0.3) + (6.76 脳 0.1) + (21.16 脳 0.4) = 5.832 + 3.468 + 0.676 + 8.464 = 18.44$

Standard Deviation= $蟽$

$蟽 = \sqrt{18.44} = 4.294$

Hence, $渭 = 15.4, 蟽^{2} = 18.44$ and $蟽 = 4.294$ .

When p(x<15)

$p (x < 15) = p (x = 10) + p (x = 12) = 0.2 + 0.3 = 0.5$

Hence, $P (x < 15) = 0.5$

Calculating the value when μ±2σ

The interval is

$渭卤 2 蟽 = 15.4 卤 (2 脳 4.294) = 15.4 卤 8.588 = (6.812, 23.988)$

Calculating P (x) when μ±2σ

$P (6.812 鈮� x 鈮� 23.988) = P (0 鈮� x 鈮� 17.176) = 1 - P (x 鈮� 17.176) = 1 - [P (x = 18) + P (x = 20)] = 1 - (0.1 + 0.4) = 1 - 0.5 = 0.5$

Hence, the required probability is 0.5.

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Sample 1	Sample 2
$\begin{array}{l} {\overset{炉}{x}}_{1} =5,275 \\ 蟽_{1} =150 \end{array}$	$\begin{array}{l} {\overset{炉}{x}}_{2} =5,240 \\ 蟽_{2} =200 \end{array}$

91影视

Consider the discrete probability distribution shown here.
x
10
12
18
20
p
.2
.3
.1
.4
a. Calculate $渭, 蟽^{2}$ and $蟽$ .
b. What is $P (x < 15)$ ?
c. Calculate $渭卤 2 蟽$ .
d. What is the probability that xis in the interval $渭卤 2 蟽$ ?

Short Answer

Step by step solution

Given information

Identifying the type of random variable

When p(x<15)

Calculating the value when μ±2σ

Calculating P (x) when μ±2σ

One App. One Place for Learning.

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91影视

Consider the discrete probability distribution shown here. x10121820 p.2.3.1.4a. Calculate渭,蟽2 and蟽 .b. What isP(x<15) ?c. Calculate 渭卤2蟽 .d. What is the probability that xis in the interval 渭卤2蟽 ?

Short Answer

Step by step solution

Given information

Identifying the type of random variable

When p(x<15)

Calculating the value when μ±2σ

Calculating P (x) when μ±2σ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Discrete Mathematics

Statistics

Decision Maths

Pure Maths

Geometry

Study anywhere. Anytime. Across all devices.

Consider the discrete probability distribution shown here.
x
10
12
18
20
p
.2
.3
.1
.4
a. Calculate $渭, 蟽^{2}$ and $蟽$ .
b. What is $P (x < 15)$ ?
c. Calculate $渭卤 2 蟽$ .
d. What is the probability that xis in the interval $渭卤 2 蟽$ ?