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Math Help - statistic question i don't know what the answer is- please help

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    statistic question i don't know what the answer is- please help

    statistic question i don't know what the answer is- please help

    a consumer survey indicates that the average household spends an average of $155 on groceries each week. The distribution of spending amounts is approximately normal with a standard deviation of $25. Based on this distribution.
    a- what proportion of the population spends more then $175 dollars per week on groceries?
    b- what is the probability of randomly selecting a family that spends less than $100 per week on groceries?
    c- how much money do you need yo spend on groceries watch week to be in the top 20% of the distribution?
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    Quote Originally Posted by sf415415 View Post
    statistic question i don't know what the answer is- please help

    a consumer survey indicates that the average household spends an average of $155 on groceries each week. The distribution of spending amounts is approximately normal with a standard deviation of $25. Based on this distribution.
    a- what proportion of the population spends more then $175 dollars per week on groceries?
    b- what is the probability of randomly selecting a family that spends less than $100 per week on groceries?
    c- how much money do you need yo spend on groceries watch week to be in the top 20% of the distribution?
    (a) Calculate Pr(X > 175) = Pr( Z > 0.8) since Z = \frac{x - \mu}{\sigma} = \frac{175 - 155}{25} = 0.8.

    Note that Pr(Z > 0.8) = 1 - Pr(Z < 0.8).


    (b) Calculate Pr(X < 100).


    (c) Find the value of a such that Pr(X > a) = 0.2.

    To do this, find the value z* of Z such that Pr(Z > z*) = 0.2. Note that Pr(Z > z*) = 0.2 => Pr(Z < z*) = 0.8.

    Then substitute z* ito z* = \frac{a - 155}{25} and solve for a.
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