Question

Company A packages bolts in boxes that are normally distributed with a mean of 312 bolts and a standard deviation of 4.1 bolts. Company B packages bolts in boxes that are normally distributed with a mean of 288 bolts and a standard deviation of 3.9 bolts. Which company is more likely to produce a box of exactly 300 bolts? Explain your answer using z-scores.

Answer 1

Company A packages bolts in boxes that are normally distributed with a mean of 312 bolts and a standard deviation of 4.1 bolts.

Company B packages bolts in boxes that are normally distributed with a mean of 288 bolts and a standard deviation of 3.9 bolts.

Now, we have to find which company is more likely to produce exactly 300 bolts.

Now, we have to use z-scores to find this out.

We know that the formula for z-score is given by

Where,

x is the observed value

m is the mean

s is the standard deviation

So, for company A, the z-score is

And, for company B, the z-score is

Now, we find that, for Company A, the z-score is more likely than the z-score for Company B.

So, Company A is more likely to produce exactly 300 bolts.