Solution Found!

Statistics / Applied Statistics and Probability for Engineers 6 / Chapter 4.6 / Problem 73E

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

Change Question

An article in Knee Surgery Sports Traumatol Arthrosc

Chapter 4, Problem 73E

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Problem 73E

An article in Knee Surgery Sports Traumatol Arthrosc [“Effect of Provider Volume on Resource Utilization for Surgical Procedures” (2005, Vol. 13, pp. 273–279)] showed a mean time of 129 minutes and a standard deviation of 14 minutes for anterior cruciate ligament (ACL) reconstruction surgery at high volume hospitals (with more than 300 such surgeries per year).

(a) What is the probability that your ACL surgery at a high volume hospital requires a time more than two standard deviations above the mean?

(b) What is the probability that your ACL surgery at a high volume hospital is completed in less than 100 minutes?

(c) The probability of a completed ACL surgery at a high-volume hospital is equal to 95% at what time?

(d) If your surgery requires 199 minutes, what do you conclude about the volume of such surgeries at your hospital? Explain.

Questions & Answers

QUESTION:

Problem 73E

An article in Knee Surgery Sports Traumatol Arthrosc [“Effect of Provider Volume on Resource Utilization for Surgical Procedures” (2005, Vol. 13, pp. 273–279)] showed a mean time of 129 minutes and a standard deviation of 14 minutes for anterior cruciate ligament (ACL) reconstruction surgery at high volume hospitals (with more than 300 such surgeries per year).

(a) What is the probability that your ACL surgery at a high volume hospital requires a time more than two standard deviations above the mean?

(b) What is the probability that your ACL surgery at a high volume hospital is completed in less than 100 minutes?

(c) The probability of a completed ACL surgery at a high-volume hospital is equal to 95% at what time?

(d) If your surgery requires 199 minutes, what do you conclude about the volume of such surgeries at your hospital? Explain.

ANSWER:

Solution 73E

Step1 of 5:

Let us consider a random variable X it presents the time for an ACL reconstruction surgery at high volume hospitals. Also we have mean $\mu{}=129,$ and standard deviation $\sigma{}=14.$

Here our goal is:

a). We need to find $P(X>\mu{}+2\sigma{}).$

b). We need to find $P(X<100).$

c). We need to find the value of x, when $P(X<x)=0.95.$

d). We need to find $P(X\geq{}199).$

Step2 of 5:

a).

Consider,

$P(X>\mu{}+2\sigma{})=P(X-\mu{}>2\sigma{})$

$=P(\frac{X-\mu{}}{\sigma{}}>2)$

$=P(Z>2)$

$=1-P(Z\leq{}2)$

$=1-\varphi{}(2)$

Where, $\varphi{}(2)$ is obtained from standard normal table(area under normal curve).

$\varphi{}(2)=0.9772$ (In area under normal curve we have to see in row 2.0 under column 0.00)

Hence,

$P(X>\mu{}+2\sigma{})=1-\varphi{}(2)$

$=1-0.9772$

Study Tools You Might Need

Chapter: 13 Problem: 85P

Introductory Chemistry 5
To what volume should you dilute 25 mL of a 12 M stock HCl solution to obtain a 0.500 M HCl solution?

Chapter: 3 Problem: 76P

Principles of General Chemistry 2
How many grams of solid barium sulfate form when 35.0 mL of 0.160 M barium chloride reacts with 58.0 mL of 0.065 M sodium sulfate? Aqueous sodium chloride forms also.

Chapter: 12 Problem: 35P

Principles of General Chemistry 2
Problem 35P Use MO diagrams and the bond orders you obtain from them to answer: (a) Is Be2+ stable? (b) Is Be2+ diamagnetic? (c) What is the outer (valence) electron configuration of Be2+?

Chapter: 8 Problem: 7

Physics: Principles with Applications 6
A grinding wheel 0.35 m in diameter rotates at 2500 rpm. Calculate its angular velocity in rad/s. (b) What are the linear speed and acceleration of a point on the edge of the grinding w heel?

Chapter: 11 Problem: 3

Campbell Biology 10
. Lipid-soluble signaling molecules, such as aldosterone, cross the membranes of all cells but affect only target cells because a. only target cells retain the appropriate DNA segments. b. intracellular receptors are present only in target cells. c. only target cells have enzymes that break down aldo

Chapter: 44 Problem: 1

Campbell Biology 10
Unlike an earthworms metanephridia, a mammalian nephron a. is intimately associated with a capillary network. b. functions in both osmoregulation and excretion. c. receives filtrate from blood instead of coelomic fluid. d. has a transport epithelium.

Chapter: 14 Problem: 1

Principles of Accounting, Volume 1: Financial Accounting
Which of the following is not a characteristic that sets preferred stock apart from common stock? A. voting rights B. dividend payments C. transferability D. ownership

Chapter: 11 Problem: 2

Advanced Engineering Mathematics 10
What are the Euler formulas? By what very important idea did we obtain them?

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account