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31 December, 21:40

Company A packages roofing nails and boxes that are normally distributed with a mean of 272 nails and a standard deviation of 5.4 nails.

Company B packages roofing nails in boxes that are normally distributed with a mean of 249 nails and a standard deviation of 3.8 nails

Which company is more likely to produce a box of 260 roofing nails?

explain your answer using Z

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  1. 31 December, 21:52
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    Company B is more likely to produce a box of 260 roofing nails.

    Step-by-step explanation:

    Company A:

    Mean = 272 nails

    Standard deviation = 5.4 nails

    Roofing nails expected to be produced = 260

    ⇒ 260 = 272 + z * 5.4

    ⇒ z = - 2.222

    Hence, Company A has a chance of 1.32% of producing exactly or fewer than 260 boxes of roofing nails.

    Company B:

    Mean = 249 nails

    Standard deviation = 3.8 nails

    Roofing nails expected to be produced = 260

    ⇒ 260 = 249 + z * 4.8

    ⇒ z = 2.895

    Hence, Company B has a chance of 0.19% of producing exactly or more than 260 boxes of roofing nails.

    Therefore, Company B is more likely to produce a box of 260 roofing nails.
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