Question

2. Company A packages roofing nails in boxes that are normally distributed with a mean of 276 nails and a standard deviation of 5.8 nails. Company B packages roofing nails in boxes that are normally distributed with a mean of 252 nails and a standard deviation of 3.4 nails. Which company is more likely to produce a box of 260 roofing nails? Explain your answer using z-scores.

Answer 1

Company B

Explanation:

We would use z score formula

z = (x - μ) / σ

x = raw score

μ = mean

σ = Standard deviation

let x = 260 with the mean μ1 = 276 and standard deviation σ = 5.8

let x = 260 with the mean μ2 = 252 and standard deviation σ = 3.4

z1 = (x- μ1) / σ = (260- 276) / 5.8 = -2.7586206897

z2 = (x2 - μ) / σ = (260 -252) / 3.4= 2.3529411765

Comparing the two z scores, we can see that company B has the probability of producing 260 nails because it has a positive z score of approximately 2.35 compared to company A with a z score of -2.76.