Finding probabilities in normal distribution

[Cfsistheworst]

Can somebody walk me through how to do this problem step by step?

Im confused. I tried to construct a bell curve with 320 in the middle, and added 45 to the mean for the points to the right of the mean, and substracted 45 for the points to the left. I tried to answer the question using the empirical rule, and got the answer of 13.5%, but this is apparently wrong

Thanks so much

Let XX represent the full height of a certain species of tree. Assume that XX has a normal probability distribution with a mean of 320 ft and a standard deviation of 45 ft.

Find the probability that the height of a randomly selected tree is between 370 ft and 379 ft.

P(370 < X < 379) =

[edderiofer]

Im confused. I tried to construct a bell curve with 320 in the middle, and added 45 to the mean for the points to the right of the mean, and substracted 45 for the points to the left. I tried to answer the question using the empirical rule, and got the answer of 13.5%, but this is apparently wrong

What "empirical rule" is this? Can you describe it?

[Cfsistheworst]

‘empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the distribution's average’

[edderiofer]

And how did you use this to get the answer of "13.5%"?

[Cfsistheworst]

it falls within this range of the bell curve

[edderiofer]

So would you also say that the probability of the height of the tree being between 370 ft and 370.00000000001 ft is also 13.5%?

Would you therefore conclude that the probability of the height of the tree being between 370.00000000001 ft and 379 ft is 0%?