The lengths of a certain species of fish were found to be normally distributed. The mean length is 79 cm with a standard deviation of 10 cm. In a school of 310 of these fish, about how many would be longer than 69 cm?

Question

Ineedhelponmymath · Answer

I have the multiple-choice answers down below
105 fish
42 fish
260 fish
302 fish

Ineedhelponmymath · Answer

260?

SmokeyBrown · Answer

I was wrong
Based on a standard distribution, about 34% of the population should be between the mean and 1 standard deviation less than the mean.
So, 34% of the school of 310 should be between 69 cm and 79 centimeters. Then another 50% should be larger than 79 centimeters, since that would be in the middle of the distribution.
In total, about 84% of the fish should be longer than 69 cm.
Out of 310, how many is that?

SmokeyBrown · Answer

And you're right! That does come out to be about 260 fish, well done.

And welcome to QuestionCove, btw :)

Ineedhelponmymath · Answer

Thank you so much. I have questions. Is it okay if i post them here with you? Its all good if you cant. there is 6 more questions left