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

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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