Results 1 to 2 of 2

Math Help - Probability of passing inspection

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    3

    Probability of passing inspection

    Okay here it is:

    In a southern statek, it was revealed that 5% of all automobiles in the state did not pass inspection. Of the next ten automobiles entering the inspection station,
    a. what is the probability that none will pass inspection?
    b. the probability that all will pass?
    c. the probability that exactly 2 will not pass?
    d. the probability that more than 3 will not pass?
    e. the probaility that fewer than two will not pass?

    Thanks to anyone who provides help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Nov 2008
    Posts
    61
    This is a binomial distribution. Let X be the number of trucks that do NOT pass inspection. Then for ten trucks we have:

    P(X=x)=\begin{pmatrix} 10 \\ x \end{pmatrix} (0.05)^x(0.95)^{10-x}

    a) We need to find P(X=10):

    P(X=10)=\begin{pmatrix} 10 \\ 10 \end{pmatrix} (0.05)^{10}(0.95)^{10-10}

    P(X=10)=9.77 \times 10^{-14}

    b and c are pretty much the same, just set X=0 and X=2, respectively.

    d) This one's a little different. We need to find P(X>3). This is equivalent to 1-P(X \le 3). The latter is easier to calculate so let's do that one.

    P(X>3)=1-P(X\le 3)

    P(X>3)=1-P(X=0)-P(X=1)-P(X=2)-P(X=3)

    From here just plug in the appropriate values in the formula and you'll get your answer.

    e is pretty similar to d, just find P(X<2)=P(X=0)+P(X=1)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: July 8th 2010, 09:10 PM
  2. Probability of passing a quiz
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 3rd 2010, 10:13 AM
  3. Probability of students passing med school
    Posted in the Statistics Forum
    Replies: 2
    Last Post: October 14th 2009, 01:38 PM
  4. by inspection
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 11th 2009, 07:36 AM
  5. by inspection
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: January 6th 2009, 01:15 PM

Search Tags


/mathhelpforum @mathhelpforum