Records show that the probability is 0.00006 that a car will have a flat tire while driving through a certain tunnel.Find the probability that at least 2 of 10,000 cars passing through this channel will have flat tires?

1 Answer
1s2s2p
Apr 13, 2018

#0.1841#

Explanation:

Firstly, we start with a binomial: #X~B(10^4,6*10^-5)#, even though #p# is extremely small, #n# is massive. Therefore we can approximate this by using normal.

For #X~B(n,p);Y~N(np,np(1-p))#

So, we have #Y~N(0.6,0.99994)#

We want #P(x>=2)#, by correcting for normal using bounds, we have #P(Y>=1.5)#

#Z=(Y-mu)/sigma=(Y-np)/sqrt(np(1-p))=(1.5-0.6)/sqrt(0.99994)~~0.90#

#P(Z>=0.90)=1-P(Z<=0.90)#

Using a Z-table, we find that #z=0.90# gives #P(Z<=0.90)=0.8159#

#P(Z>=0.90)=1-P(Z<=0.90)=1-0,8159=0.1841#

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