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Math Help - Stats probability question

  1. #1
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    Stats probability question

    At supermarkets the sales of canned tuna varies from week to week.
    Marketing researchers have determined that there is a relationship between sales of canned tuna and the price of canned tuna. Specifically,

    SALES = 40710 -430PRICE where SALES are cans sold per week and PRICE is measured in cents per can. Suppose
    PRICE over the year can be considered (approximately) a normal random variable with mean
    μ=75 cents and standard deviation σ = 5 cents. That is PRICE ~ N(75,5).
    i) What is the numerical expected value of SALES? Show your work.
    ii) What is the numerical value of the variance of SALES? Show your work.
    iii) Find the probability that more than 6300 cans are sold per week. Draw a sketch to
    illustrate your calculation.










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  2. #2
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    Re: Stats probability question

    Can anyone show working to solve questions above. Thanks
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  3. #3
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    Re: Stats probability question

    The expected value of sales is the number of sales that occurs at the expected value (mean) of price.
    Sales is related to 430 times price so the standard deviation of sales is 430 times the standard deviation of price.
    From parts (i) and (ii) you have enough information to find how many standard deviations 6300 is away from the mean. Do you know how to proceed from there?
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  4. #4
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    Re: Stats probability question

    Hi I no how to do i and ii being 8460 and 4622500, but not sure how to do iii P[Z> (6300 - 8460)/2150=-1.004 15.87%

    Please correct, me cheers
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  5. #5
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    Re: Stats probability question

    You should have said you only needed help with the third. You got the value of Z correctly, have you been taught how to use tables for the normal distribution? Tables normally give you how much of the distribution is below Z but you are interested in how much of the distribution is above Z (greater than 6300). You should know that 1-(probability below Z)= (probability above Z)
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