a. To determine Find the probability that a patient stays in hospital for less than 5.5 days. Explanation Calculation: The given information is that the length of stay of each patient in the department is exponentially distributed with mean 7 days. The random variable X follows the exponential distribution with parameter λ . Then the probability density function is, f ( x ) = λ e − λ x for x > 0 The random variable X is defined as the length of stay of each patient in the department. Then X follows Exponential distribution with mean 7 days. Calculate the probability that a patient stays in hospital for less than 5.5 days is P ( X < 5.5 ) . Then, P ( X < 5.5 ) = 1 − P ( X > 5.5 ) P ( X > 5.5 ) = ∫ 5 b. To determine Find the probability that a patient stays in hospital for more than 10.0 days if the patient has currently stayed for 7.0 days. c. To determine Find mean length of stay if the probability that a patient stays in the hospital less than 6.0 days is 0.9.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

See similar textbooks

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Videos

Question

Chapter 4.8, Problem 135E

To determine

Find the probability that a patient stays in hospital for less than 5.5 days.

To determine

Find the probability that a patient stays in hospital for more than 10.0 days if the patient has currently stayed for 7.0 days.

To determine

Find mean length of stay if the probability that a patient stays in the hospital less than 6.0 days is 0.9.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.8, Problem 134E

Chapter 4.8, Problem 136E

Students have asked these similar questions

Question 2: When John started his first job, his first end-of-year salary was $82,500. In the following years, he received salary raises as shown in the following table. Fill the Table: Fill the following table showing his end-of-year salary for each year. I have already provided the end-of-year salaries for the first three years. Calculate the end-of-year salaries for the remaining years using Excel. (If you Excel answer for the top 3 cells is not the same as the one in the following table, your formula / approach is incorrect) (2 points) Geometric Mean of Salary Raises: Calculate the geometric mean of the salary raises using the percentage figures provided in the second column named “% Raise”. (The geometric mean for this calculation should be nearly identical to the arithmetic mean. If your answer deviates significantly from the mean, it's likely incorrect. 2 points) Hint for the first part of question 2: To assist you with filling out the table in the first part of the question,…

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile range, variance, and standard deviation (to a maximum of 2 decimals, if decimals are necessary). Range Interquartile range Variance Standard deviation

Perform a Step by step following tests in Microsoft Excel. Each of the following is 0.5 points, with a total of 6 points. Provide your answers in the following table. Median Standard Deviation Minimum Maximum Range 1st Quartile 2nd Quartile 3rd Quartile Skewness; provide a one sentence explanation of what does the skewness value indicates Kurtosis; provide a one sentence explanation of what does the kurtosis value indicates Make a labelled histogram; no point awarded if it is not labelled Make a labelled boxplot; no point awarded if it is not labelled Data 27 30 22 25 24 22 20 28 20 26 21 23 24 20 28 30 20 28 29 30 21 26 29 25 26 25 20 30 26 28 25 21 22 27 27 24 26 22 29 28 30 22 22 22 30 21 21 30 26 20

Chapter 4 Solutions

Applied Statistics and Probability for Engineers

Ch. 4.2 - 4-1. Suppose that f(x) = e−x for 0 < x. Determine...Ch. 4.2 - 4-2. Suppose that f (x) = 3(8x – x2)/256 for 0< x...Ch. 4.2 - 4-3. Suppose that f (x) = 0.5 cos x for −π/2 < x <...Ch. 4.2 - Prob. 4E Ch. 4.2 - 4-5. Go Tutorial Suppose that for 3 < x < 5....Ch. 4.2 - Prob. 6E Ch. 4.2 - 4-7. Suppose that f(x) = 1 .5x2 for −1 < x < 1....Ch. 4.2 - 4-8. The probability density function of the time...Ch. 4.2 - 4-9. The probability density function of the net...Ch. 4.2 - Prob. 10E

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.