2.Suppose the defective rate at a particular factory is 1%. Suppose 50 partswere selected from the daily output of parts. Let X denote the number ofdefective parts in the sample.a)Find the probability that the sample contains exactly 2 defective parts.b)Use Poisson approximation to find the probability that the sample containsexactly 2 defective parts.c)Find the probability that the sample contains at most 1 defective part.d)Use Poisson approximation to find the probability that the sample containsat most 1defective part.

Givenp=0.01n=50Let "x" be the number of defective parts in the…

Answered: Suppose the defective rate at a…

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...

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18 - The lifetime of the phones produced in factory A is 2900 days. The phones produced in factory B have a lifespan of 2600 days. A sample of 50 telephones was taken from factories A and B. Since the standard error of the difference between the sample averages of the phone lifetimes is 25.49, what is the probability that the mean of the sample from factory A will be more than 325 days from the mean of the sample from factory B?A) 0.1635 B) 0.483 C) 0.237 D) 0.331 E) 0.95
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a) is the maximum probability of making a Type I error that we are willing to accept b) is the same as the population proportion, p c) measures the number of standard deviations from the mean d) is the probability of making a Type II error e) is the same as alpha
6) A standard normal random variable has µ = 0 and a standard deviation σ = 1. Use Table 3 to find the probability less than 2.22. 7) A standard normal random variable has µ = 0 and a standard deviation σ = 1. Use Table 3 to find the probability greater than 3.28. 8) A standard normal random variable has µ = 0 and a standard deviation σ = 1. Use Table 3 to find the probability between -1.00 and -2.50.
4. Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 1 using the Kaplan-Meir approach and interpret the results. Time in years Number at risk Nt Number of deaths, Dt Number of censored Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 A) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85.B) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study.C) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment.D) The probability of surviving 1 year after being diagnosed with a slow-progressing form of…
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3. The average number of phone inquiries per day at the poison control center is 4. Use the Poisson approximation. i) Find the probability it will receive 5 calls on a given day. ii) Find the probability it will receive at least 1 call on a given day.
A variable is normally distributed with mean 12 and standard deviation 4 a.) find the percentage of all possible values of the variable that lie between 4 and 16 b.) find the percentage of all possible values of the variable that exceed 6 c.)find the percentage of all possible values of the variables that are less than 2
The times between arrivals in a queue follow an exponential distribution with a rate of 1. Check the incorrect alternative: a) 50% of arrivals will take place before 1 minute. b) If the times between arrivals are exponentially distributed with a rate equal to 1, then arrivals occur according to a Poisson distribution with an average equal to 1. c) Times between arrivals are independent. d) The variance of the times between arrivals is equal to 1. e) There is an average of one arrival every minute.
11. The probability that a mouse inoculated with a serum will contract a certain disease is 0.02. Using The Poisson approximation, find the probability taht at most 3 of 30 inoculated mice will contract the disease.
Assume that the height, X, of a college woman is a normally distributed random variable with a mean of 65 inches and a standard deviation of 3 inches. Suppose that we sample the heights of 180 randomly chosen college women. Let M be the sample mean of the 180 height measurements. Let S be the sum of the 180 height measurements. All measurements are in inches. Using R and write the code out.a) What is the probability that X < 59? b) What is the probability that X > 59? c) What is the probability that all of the 180 measurements are greater than 59? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-180*65 >10? g) What is the standard deviation of S-180*65 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >65.41? k) What is the standard deviation of 180*M? l) If the probability of X > k is equal to .3, then what is k?
Auto vehicles arrive at a petrol pump with one petrol unit in Poisson fashion, averaging 10 units per hour. The service time is distributed exponentially with a mean of 3 minutes. Find the following:a) Average number of units in the systemb) Average waiting time for customersc) The average length of the queued) The probability that a customer arriving at the pump will have to wait.e) The utilization factor for the petrol pumpf) The probability that the number of customers in the system is 2.

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