SOLUTION: 1.According to company records, 5% of all automobiles brought to Geoff's Garage last year for a state-mandated annual inspection did not pass. Of the next 10 automobiles entering t

Question 1197433: 1.According to company records, 5% of all automobiles brought to Geoff's Garage last year for a state-mandated annual inspection did not pass. Of the next 10 automobiles entering the inspection station,
a. what is the probability that none will pass inspection?
c. what is the probability that exactly 2 will not pass inspection?
My Work:
a. n=10, x=0, p=0.05
f(x)=10!/10! (10-0)! * 0.05^0*(1-0.05)^10-0
f(x)= 1/1*1(0.95)^10
f(x)=0.598736923838 wrong
c.n=10, p=0.05, x=10-2=8
f(x)=10!/8!(10-8)!*.05^8(1-.05)^(10-8)
=45*2.79310221^-7
=0.00001256895 wrong

Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

I appreciate you showing your work and thought process.

Part (a)

You have "passed inspection" and "did not pass inspection" mixed up.

The 5% refers to vehicles that did not pass.
So you'll use x = 10, where x is the number of vehicles that didn't pass.

Some calculators will display this as 9.765625E-14
The uppercase E refers to "ten to the" where we then specify the exponent after the 10.

To convert this to standard notation, we move the decimal point 14 spots to the left to go from 9.765625 to
0.000 000 000 000 097 656 25
The spacing between the digits is to make the number more readable. Otherwise it would look like this
0.00000000000009765625

Since the number is so incredibly small, it's better to use scientific notation. It'll avoid the tedious pain of having to write out all of those zeros. There are 13 zeros between the decimal point and the digit 9.

===================================================================

Part (b)

This time we use x = 2 so we can determine the probability exactly 2 cars not passing inspection.

The answer is approximately 0.07463479852001

Round that value however your teacher instructs.

Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.

            As I see from your post, you are a beginner in solving problems on binomial distributuon probability.

            At this site, there are lessons that present a wide collection of solved problems of this type.

            Look at these lessons - you will feel yourself more confident and your horizon will quickly become wider.

The links to these lessons are

    - Simple and simplest probability problems on Binomial distribution
    - Typical binomial distribution probability problems

It is free of charge and without registration, and it works better than any teacher, an online or a private.

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