Q96E Assume that x is a binomial rand... [FREE SOLUTION]

91影视

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: Q96E (page 452)

Assume that x is a binomial random variable with n = 1000 andp = 0.50. Use a normal approximation to find each of the following probabilities:
a. $P (x > 500)$
b. $P (490 鈮� x < 500)$
c. $P (x > 550)$

Short Answer

Expert verified

$P (x > 500) = 0.50$
$P (490 鈮� x 鈮� 500) = 0.2357$

c. $P (x > 550) = 0.0008$

Step by step solution

Given information

x be binomial distribution with n = 1000 and p= 0.50

Calculation for the z value

$\begin{array}{l} 渭 = n p \\ = 1000 脳 0.50 \\ = 500 \end{array}$

$蟽 = \sqrt{n p (1 - p)} = \sqrt{1000 脳 0.50 脳 (1 - 0.50)} = \sqrt{1000 脳 0.50 脳 0.50} = 15.8114$

So,

$\begin{array}{l} z = \frac{x - 渭}{蟽} \\ = \frac{x - 500}{15.8114} \end{array}$

Probability calculation P(x>500)

$P (x > 500) = 1 - P (x < 500) = 1 - P (z < 0) = 1 - 0.50 = 0.50 P (x > 500) = 0.50$

Therefore, the required probability is 0.50.

Probability calculation P(490≤x<500)

$P (490 鈮� x < 500) = P (< 500) - P (x 鈮� 490) = P (z < 0) - P (z 鈮� - 0.6325) = P (z < 0) - (1 - P (z 鈮� - 0.6325)) = 0.50 - (1 - 0.7357) = 0.2357 P (490 鈮� x < 500) = 0.2357$

Therefore, the probability is 0.2357.

Probability calculation P(x>550)

$P (x > 550) = 1 - P (x > 550) = 1 - P (z < 3.1623) = 1 - 0.999217 = 0.000783 鈮� 0.0008 P (x > 550) = 0.0008$

Therefore, the probability is 0.0008.

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91影视

Assume that x is a binomial random variable with n = 1000 andp = 0.50. Use a normal approximation to find each of the following probabilities:
a. $P (x > 500)$
b. $P (490 鈮� x < 500)$
c. $P (x > 550)$

Short Answer

Step by step solution

Given information

Calculation for the z value

Probability calculation P(x>500)

Probability calculation P(490≤x<500)

Probability calculation P(x>550)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

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91影视

Assume that x is a binomial random variable with n = 1000 andp = 0.50. Use a normal approximation to find each of the following probabilities:a. P(x>500)b.P(490鈮�x<500)c.P(x>550)

Short Answer

Step by step solution

Given information

Calculation for the z value

Probability calculation P(x>500)

Probability calculation P(490≤x<500)

Probability calculation P(x>550)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Decision Maths

Pure Maths

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Assume that x is a binomial random variable with n = 1000 andp = 0.50. Use a normal approximation to find each of the following probabilities:
a. $P (x > 500)$
b. $P (490 鈮� x < 500)$
c. $P (x > 550)$