During a life expectance test of 20 light bulbs, the failure time are recorded as 4, 6, 18, 42, 50, ... (hours). Formulate the following tables from the failure data e. Failure density function, f(t) f hazard function, Z(t) g. Failure cumulative distribution function, F(t) h. Success rate (Reliability), R(t) i. Mean Time To Fail, MTTF j. The Overall Mean Time To Fail, MTTF (overall)

During a life expectance test of 20 light bulbs, the failure time are recorded as 4, 6, 18, 42, 50, ... (hours). Formulate the following tables from the failure data e. Failure density function, f(t) f hazard function, Z(t) g. Failure cumulative distribution function, F(t) h. Success rate (Reliability), R(t) i. Mean Time To Fail, MTTF j. The Overall Mean Time To Fail, MTTF (overall)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Discuss quartiles and their importance.
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 40 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,250 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,250 lb / 40 = 163 lb. What is the possiblity that the aircraft is overloaded? Should the pilot take any action to correct an overloaded aircraft? Assume that the weights of men are normally distributed with a mean of 177.3 lb and a standard deviation of 39.3 The probability is approximately
Data are collected in an experiment designed to in- vestigate the impact of different positions of the mother during ultrasound on fetal heart rate. Fetal heart rate is measured by ultrasound in beats per minute. The study includes 20 women who are as- signed to one position and have the fetal heart rate measured in that position. Each woman is between 28 weeks and 32 weeks gestation. The data are shown in Table 7–7. Is there a significant difference in mean fetal heart rates by position? Run the test at a 5% level of significance. back side sitting standing 140 141 144 147 144 143 145 145 146 145 147 148 141 144 148 149 139 136 144 145
what is the tird quartile
A researcher is interested in testing the relationship between smoking and BMI (kg/m2) in adults aged 30-45. In order to test this association, the researcher divides smoking into currently more than a pack a day, currently less than a pack a day, and never smokers. The following table represents the BMIs for each participant enrolled by their respective smoking category. Current Smoker (≥1pack/day) Current Smoker (<1 pack/day Never Smoked 26.7 29.4 22.1 29.4 28.6 30.4 24.3 27.4 21.3 28.4 23.2 26.4 21.6 20.1 19.7 27.4 20.6 19.8 26.8 19.7 21.6 36.4 19.6 22.3 31.5 21.6 24.3 27.4 21.5 *Continue as though all assumptions for ANOVA are met. A) Calculate the MSW and MSB for the data represented above. B) Carry out a formal test for a one-way analysis of variance among the groups and interpret your results.
5. Oxygen demand is a term blologists use to describe the axygen needed by fish and other aquatic organisms for survval. The Environmental Protection Agency conducted a study of a wetland area in Marin County, Californla. In this wetland environment, the mean oxygen demand was u=9.9 mg/L, and a= 1.7 mg/L. (Reference: EPA Report 832-R- 93- 005). Let x be a random varlable that represents oxygen demand in this wetland environment. Assume x has a probability distribution that is approximately normal. a. An oxygen demand below 8 mg/L Indicates that some organisms In the wetland environment may be dying. What is the probability that the oxygen demand will fall below 8 mg/L? b. A high oxygen demand can also indicate trouble. An oxygen demand above 12 mg/L may indicate an overabundance of organisms that endanger some types of plant life. What is the probability that the oxygen demand will exceed 12 mg/L?
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 42 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,056 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 7,056 lb42=168 lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 178.3 lb and a standard deviation of 36.8.
One tree in the study had a weight that exceeded its expected weight (according to the best fit curve) by more than that of any other tree. By how many tons did the trees actual weight exceed the expected weight for its height?
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 43 passengers, and a flight has fuel and baggage that allows for a total passenger load of 7,009 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 7,009 lb / 43 =163 lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 182.4 lb and a standard deviation of 38.4.
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 37 passengers, and a flight has fuel and baggage that allows for a total passenger load of 5,994lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 5,994/37lb=162lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that weights of men are normally distributed with a mean of 181.6lb and a standard deviation of 36.2. The probability is approximately?
Before every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 42 passengers, and a flight has fuel and baggage that allows for the total passenger load of 6,972lb. The pilot sees that the plane is full and all the passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,972lb/42=166lb. What is the probability that the aircraft is overloaded? Should the pilot take any action to correct for an overloaded aircraft? Assume that the weights of men are normally distributed with a mean of 176.9lb and a standard deviation of 37.7. THE probability is approximately. ? Round to four decimal places.
Case scenario: A cohort study involved an assessment of the relationship between cigarette smoking and incuof lung cancer. For cigarette smokers, the lung cancer incidence rate was Iexp = 200 per 100,000. For nonsmokers, the lung cancer incidence rate was Iunexp = 25 per 100,000. The lung cancer incidence rate in the entire population was Itotal = 100 per 100,000. A) what is the relative risk (risk ratio) of developing lung cancer? Interpret this value in plain language? B) calculate the attributable risk and interpret this value in plain language? C) calculate the attributable-risk percent and interpret this value in plain language? D) is cigarette smoking a risk factor for lung cancer? Explain your answer. E) Hypothetically speaking, if cigarette smoking could be eliminated from this population, what percentage of lung cancer could be avoided?