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    I am struggling on a Probabilty question about paint being applied to cars.

    The table needed is as follows:

    _____________Mean ____Standard Deviation
    Primer_________3.7__________1.2
    Undercoat______3.9__________0.9
    Top Coat_______4.0__________0.75

    (I hope it is easy to follow)

    My questions about this are:

    1. How do I find the total amount of paint used on average on each car?

    2. What percentage of cars will use less than 3 litres of Top Coat?

    3. The probability that a car, selected at random, will use between 2.3 litres and 4.5 litres of undercoat?

    4. What percentage of cars will use more than 3.2 litres of Primer?

    5. If a car receives less than 2 litres of top coat there is a quality issue about this paintwork. The company requires that no more than 2% of the cars should present this problem. The amount of paint dispensed can be adjusted. Determine a new mean such that this quality requirement will just be satisfied. Use an appropriate standard deviation from the table.

    We can assume that they follow a Normal Distribution

    I've been stuck on this for the past 2 days, I really cannot get my head around it for some reason.

    Thanks for any help.
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    (Original post by D556mm)
    I am struggling on a Probabilty question about paint being applied to cars.

    The table needed is as follows:

    _____________Mean ____Standard Deviation
    Primer_________3.7__________1.2
    Undercoat______3.9__________0.9
    Top Coat_______4.0__________0.75

    (I hope it is easy to follow)

    My questions about this are:

    1. How do I find the total amount of paint used on average on each car?
    The average total amount of paint use is the sum of the average amount of primer, the average amount of undercoat,...

    Thanks for any help.
    For the remainder of your questions we need to know the distribution of the amounts. Can we assume they're normally distributed?
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    (Original post by ghostwalker)
    The average total amount of paint use is the sum of the average amount of primer, the average amount of undercoat,...



    For the remainder of your questions we need to know the distribution of the amounts. Can we assume they're normally distributed?

    Yes, we can assume they are Normally Distributed. I forgot to edit that in.
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    (Original post by D556mm)
    Yes, we can assume they are Normally Distributed. I forgot to edit that in.
    So, for question 2, the top coat is distributed N(4,0.75^2) and you're interested in the probability that the amount of top coat is <=3.

    Can you work that out? And if not, say what you're stuck with.
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    (Original post by ghostwalker)
    So, for question 2, the top coat is distributed N(4,0.75^2) and you're interested in the probability that the amount of top coat is <=3.

    Can you work that out? And if not, say what you're stuck with.
    I standarized it and got a percentage of 90.82% then subtracted from 100% to then get 9.18% (seemed about right since the mean is 4)

    PS. I last did Stats 2 years ago for my 1st year at college and haven't done it since so I'm a bit rusty
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    (Original post by D556mm)
    I standarized it and got a percentage of 90.82% then subtracted from 100% to then get 9.18% (seemed about right since the mean is 4)

    PS. I last did Stats 2 years ago for my 1st year at college and haven't done it since so I'm a bit rusty
    Well, you seem to have remembered it.

    One point, depending on the accuracy of the tables/software you're using.
    A standard deviation of 1.333 gives 90.87% (in my tables). 1.33 gives 90.82%, as you had.

    Edit: Going to try and see the comet now.
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    (Original post by ghostwalker)
    Well, you seem to have remembered it.

    One point, depending on the accuracy of the tables/software you're using.
    A standard deviation of 1.333 gives 90.87% (in my tables). 1.33 gives 90.82%, as you had.

    Edit: Going to try and see the comet now.
    Even in college, I could never remember when to subtract 1 or leave it as it is from the probabilities given in the table
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    (Original post by D556mm)
    Even in college, I could never remember when to subtract 1 or leave it as it is from the probabilities given in the table
    You do need to subtract it from 1, or 100% in this case, as you did.

    A quick sketch of the normal curve and plotting the sd you're interested in may help.

    Couldn't see the comet :sad:
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    (Original post by ghostwalker)
    You do need to subtract it from 1, or 100% in this case, as you did.

    A quick sketch of the normal curve and plotting the sd you're interested in may help.

    Couldn't see the comet :sad:
    Great Thanks for all the help

    Answers for the others are in order of question:
    3. 0.71103
    4 0.66276
    5. Haven't completed yet
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    (Original post by D556mm)
    Great Thanks for all the help

    Answers for the others are in order of question:
    3. 0.71103
    4 0.66276
    5. Haven't completed yet
    I get

    3. 0.7098

    4. 0.6615
 
 
 
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