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Math Help - probability question need help

  1. #1
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    Unhappy probability question need help

    A road is constructed so that the right-turn lane at an intersection has a capacity of 3 cars. Suppose that 30% of cars approaching the intersection want to turn right, and they do so independently.

    a) if 15 cars approach the intersection, what is the probability that the right-turn lane will not hold all the cars wanting to turn right?

    b) over a week 1428 cars used the intersection
    i) what is the distribution of the sample proportion of cars turning right at this intersection, in random samples of this size?

    ii) what is the probability that, in such a sample, the proportion turning right is between 0.28 and 0.32?

    help meeeeee

    Anyone?

    is a) binomial (n=15, p=3/10)
    P(X>3)=.2969 or is there more to it then this?

    b) i) Binomial (n=1428, p=3/10)
    is there more to this?

    and what would you answer for b) ii) b?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sanja85 View Post
    A road is constructed so that the right-turn lane at an intersection has a capacity of 3 cars. Suppose that 30% of cars approaching the intersection want to turn right, and they do so independently.

    a) if 15 cars approach the intersection, what is the probability that the right-turn lane will not hold all the cars wanting to turn right?

    b) over a week 1428 cars used the intersection
    i) what is the distribution of the sample proportion of cars turning right at this intersection, in random samples of this size?

    ii) what is the probability that, in such a sample, the proportion turning right is between 0.28 and 0.32?

    help meeeeee

    Anyone?

    is a) binomial (n=15, p=3/10)
    P(X>3)=.2969 or is there more to it then this?
    That's OK

    b) i) Binomial (n=1428, p=3/10)
    is there more to this?
    That's OK

    and what would you answer for b) ii) b?
    I would use the normal approximation to the binomial here, you know the mean number and its standard deviation, just divide these by the sample size to turn into proportion and SD of the proportion etc.

    CB
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