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24 September, 03:14

32 % of U. S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is (a) exactly two, (b) more than two, and (c) between two and five, inclusive

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  1. 24 September, 03:57
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    A. 21.06%

    B. 66.88%

    C. 81.56%

    Step-by-step explanation:

    There are two possible answer for the question asked, yes (more likely to make purchases) or no. The probability for a random adults answer yes to the question is 32% so the probability that the adults answer no is 68%.

    (a) exactly two

    There is only one case for this question, 2 people say yes and 8 people say no. The calculation for this problem will be:

    2P10 * P (yes) ^2 * P (no) ^8 = 10!/2!8! * 32%^2 * 68%^8 = 0.21066 = 21.06%

    (b) more than two

    There are a lot of case for more than two, its easier to find out the negation of the probability which is "two or less". Case that fulfill "two or less" will be: 2 yes and 8 no

    1 yes and 9 no

    0 yes and 10 no

    The calculation for the negation will be:

    ~P (X) = 0P10 * P (yes) ^0 * P (no) ^10 + 1P10 * P (yes) ^1 * P (no) ^9 + 2P10 * P (yes) ^2 * P (no) ^8 =

    10!/0!10! * 32%^0 * 68%^10 + 10!/1!9! * 32%^1 * 68%^9 + 10!/2!8! * 32%^2 * 68%^8

    0.02113 + 0.09947 + 0.21066 = 0.33126 = 33.12%

    Since its the negation, you need to subtract 1 with the negation

    P (X) = 1 - ~P (X)

    P (X) = 1 - 33.12% = 66.88%

    (c) between two and five, inclusive

    Same formula as above, but the case is:

    2 yes and 8 no

    3 yes and 7 no

    4 yes and 6 no

    5 yes and 5 no

    The calculation will be:

    2P10 * P (yes) ^2 * P (no) ^8 + 3P10 * P (yes) ^3 * P (no) ^7 + 4P10 * P (yes) ^4 * P (no) ^6 + 5P10 * P (yes) ^5 * P (no) ^5 =

    10!/2!8! * 32%^2 * 68%^8 + 10!/3!7! * 32%^3 * 68%^7 + 10!/4!6! * 32%^4 * 68%^6 + 10!/5!5! * 32%^5 * 68%^5

    0.21066 + 0.26435 + 0.21770 + 0.1229 = 0.81561 = 81.56%
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