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Math Help - continuous probability distribution

  1. #1
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    continuous probability distribution

    2 questions.

    1. suppose the time T taken for a car wash is normally distributed with mean 6 minutes and standard deviation 1.5 minutes . If 1000 cars are washed, what is the probability that not more than one car takes more than 10.62 minutes?

    2. a sales contract between a manufacturer and a buyer requires 20 towels to be subjected to a water absorption test. if no more than one towel fails the test, the batch is accepted. if two or three towels fail the test, an additional 20 towels are tested. the batch is then accepted if 3 or less( out of 40) fail the test. otherwise, the batch is rejected.The lengths of 20 towels are measured and if the mean length is less than a value a specified in the contract, the batch is rejected. what should be the value of a to give a probability of 0.99 of accepting a batch with mean length 106mm and standard deviation 6mm?

    Please list out your steps and the answer of these questions ,y
    our helps to solve these two questions are highly appreciated, thank you!
    Last edited by laikarting; July 6th 2011 at 04:49 AM.
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  2. #2
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    Quote Originally Posted by laikarting View Post
    2 questions.

    1. suppose the time T taken for a car wash is normally distributed with mean 6 minutes and standard deviation 1.5 minutes . If 1000 cars are washed, what is the probability that not more than one car takes more than 10.62 minutes?

    [snip]
    Let T be the random variable "Time it takes to wash a car".
    T ~ Normal(mean = 6 minutes, sd = 1.5 minutes).
    Calculate p = Pr(T > 10.62).

    Let Y be the random variable "Number of cars that take longer than 10.62 minutes to wash".
    Y ~ Binomial(p, n = 1000).
    Calculate Pr(Y = 0) + Pr(Y = 1).

    Quote Originally Posted by laikarting View Post
    2 questions.

    [snip]

    2. a sales contract between a manufacturer and a buyer requires 20 towels to be subjected to a water absorption test. if no more than one towel fails the test, the batch is accepted. if two or three towels fail the test, an additional 20 towels are tested. the batch is then accepted if 3 or less( out of 40) fail the test. otherwise, the batch is rejected.The lengths of 20 towels are measured and if the mean length is less than a value a specified in the contract, the batch is rejected. what should be the value of a to give a probability of 0.99 of accepting a batch with mean length 106mm and standard deviation 6mm?

    Your helps to solve these two questions are highly appreciated, thank you!
    I suggest that you first draw a flow chart of the testing process. Then think about the probabilities associated with each part of the flow chart.
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    Re: continuous probability distribution

    I suggest that you first draw a flow chart of the testing process. Then think about the probabilities associated with each part of the flow chart.
    flow chart? how to do that?
    Last edited by mr fantastic; July 6th 2011 at 03:21 PM. Reason: Added quote tag.
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    Re: continuous probability distribution

    Quote Originally Posted by laikarting View Post
    flow chart? how to do that?
    Do you know what a flow chart is?

    Draw a diagram, a schematic, a picture, that represents the testing process. That lets you visualise the testing process.
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    Re: continuous probability distribution

    can you find the answers for question 1 and question 2 ?thank you
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    Re: continuous probability distribution

    Quote Originally Posted by laikarting View Post
    can you find the answers for question 1 and question 2 ?thank you
    No, that is your job. I have told you how to do them. What have you tried? Where are you still stuck?
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