The length of bolts made in factory Z is normally distributed with a mean length of 0.1630 meters and a SD of 0.0084 meters. The probability that a randomly selected bolt is between 0.1546m to and 0.1756m long is between what? My guess is in between 68%-75%. But the answer is shown as 75%-82%. Can you explain please?

Hint: what is 0.1630 - 0.0084 and 1.630 + 0.0084?

That is covering 1SD below and above the mean, which is around 68%. Confusion arises for the value .1756 which is nearly 1.5 SD above the mean. Considering 1 SD below the mean, and 1.5 SD above the mean, I thought it should have been 68-75%. It should not exceed 75% in my opinion.

I hope this makes sense

yes 0.1756 k=lies roughly 1.5 sd above the mean

So it has to be > 68%

But the < 75% part is incorrect, because

68 + 7 = 75

The first half (or the left half) b/w 1sd to 2 sd is going to have more than 7% under it as it is closer to the mean

Hope the diagram makes sense

It makes sense now. Thanks a bunch.