An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poissonrandom variable with λ = 7.5.(a) What is the probability that at most 5 cars per year will experience a catastrophe?(b) What is the probability that more than 1 car per year will experience a catastrophe? 60.6860 0.60637 0.8095 0.74408 0.8944 0.84729 0.9462 0.91610.9747 0.957410T5.56.06.57.08.00 0.00410.0025 0.00150.00090.0006 0.000320.00621 0.0266 0.0174 0.0113 0.0073 0.0047 0.00300.0884 0.0620 0.0430 0.0296 0.0203 0.0138 0.00930.2017 0.1512 0.1118 0.0818 0.0591 0.0424 0.03010.2851 0.2237 0.1730 0.1321 0.0996 0.0744 0.05500.4457 0.3690 0.3007 0.241434 0.35750.021250.52890.19120.14960.115716 0.9999 0.99980.99991.0000171.0000181920110.9890 0.9799 0.9661120.9955 0.99120.9840130.9983 0.99640.992914 0.9994 0.9986 0.9970150.9998 0.99950.998821222324PPoisson Probability Sums p(x;p)5.56.00.4497 0.37820.52650.67280.7916 0.72910.59870.87740.83050.93320.90150.94670.97300.98720.99430.99760.99960.99900.9998 0.99960.9999 0.99991.0000 1.00006.52=0fl7.57.00.92080.95730.97840.98970.99540.20680.52460.45300.3856 0.32390.66200.59250.5231 0.45570.7764 0.7166 0.6530 0.58740.86220.81590.7634 0.70608.59.00.00020.00010.0019 0.00120.3134 0.25627.58.00.88810.9362 0.9091 0.87580.9658 0.9486 0.92610.9827 0.9726 0.95850.94000.9918 0.9862 0.9780 0.96650.8487 0.8030 0.75200.83640.89810.99470.9980 0.9963 0.9934 0.98890.9992 0.9984 0.99700.9997 0.99930.9999 0.99970.9987 0.99760.99570.9995 0.99890.99800.99990.9998 0.9996 0.99911.00000.99991.00009.50.00010.00080.00420.01490.04030.08858.50.16490.26870.39180.52180.64530.99980.99991.00009.00.98230.99110.99960.99990.99991.00009.5 TT0.10.20.30.40.60.70.80 0.9048 0.81870.74080.6065 0.54880.4966 0.449310.99530.98250.96310.84420.808820.95260.937130.67030.9384 0.9098 0.87810.9989 0.9964 0.9921 0.9856 0.9769 0.96590.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.99091.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.99771.0000 1.0000 1.0000 0.9999 0.9998 0.99970.98654561.00001.00001.00000.70.80.967890 1284 0.996351011T1.01.500.36790.223110.73580.557820.91970.80883 0.9810 0.934413140.99981.000015160.1TPoisson Probability Sums Σ p(x;μ)2=00.21.00.9814 0.94730.99550.98340.99940.9999 0.99911.0000 0.99981.00000.31.52.00.13530.40600.67670.85710.42.0"0.50.99550.98580.9989 0.99580.9998 0.99891.00000.5"2.5fl3.02.50.08210.04980.28730.19910.54380.42320.7576 0.64720.8912 0.81530.9580 0.9161 0.85763.54.04.55.00.0302 0.0183 0.0111 0.00670.1359 0.09160.04040.06110.3208 0.2381 0.17360.12470.5366 0.4335 0.34230.26500.7254 0.6288 0.53210.78510.9347 0.8893 0.83110.70290.9489 0.91340.97330.9901 0.9786 0.95970.96650.98810.99620.9997 0.9989 0.99670.9999 0.9997 0.99900.9997 0.9991 0.99760.9919 0.98290.9972 0.99331.00000.99991.00000.60.99991.00003.0"3.50.90.40660.77254.04.50.44050.61600.99450.9997 0.9992 0.99800.9999 0.99970.99931.0000 0.99990.99981.00000.99991.00005.00.76220.86660.93190.96820.9863

a)Suppose a random variable x defines the number of cars per year that will experience the…

An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with λ = 7.5. (a) What is the probability that at most 5 cars per year will experience a catastrophe? (b) What is the probability that more than 1 car per year will experience a catastrophe?

An automobile manufacturer is concerned about a fault in the braking mechanism of a particular model. The fault can, on rare occasions, cause a catastrophe at high speed. The distribution of the number of cars per year that will experience the catastrophe is a Poisson random variable with λ = 7.5. (a) What is the probability that at most 5 cars per year will experience a catastrophe? (b) What is the probability that more than 1 car per year will experience a catastrophe?

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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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 215 numerical entries from the file and r = 50 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1.(i) Test the claim that p is less than 0.301. Use ? = 0.10. (a) What is the level of significance?State the null and alternate hypotheses. H0: p = 0.301; H1: p < 0.301H0: p < 0.301; H1: p = 0.301 H0: p = 0.301; H1: p > 0.301H0: p = 0.301; H1: p ≠ 0.301 (b) What sampling…
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Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Now suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 221 numerical entries from the file and r = 50 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. (i) Test the claim that p is less than 0.301. Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ho: P = 0.301; H₁: p = 0.301 Ho: P 0.301 Ho: P = 0.301; H₁: p 5 and nq > 5. O The Student's t, since np 5 and nq > 5. What is the value of the…
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