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.