Question

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?

Answer 1

Answer with explanation:

Mean length of fish = 79 cm

Standard deviation = 10 cm

Total number of fish = 310

If we arrange the total fish along a bell shaped curve ,called normal distribution

1. 68.2% of the total fish will lie along one standard deviation.Means, from 79-10=69 to 79 +10=89,68.2 % of fish population will lie.

That is , 34.1 % of fish population will lie on both side of mean in one standard deviation.

As, mean is mid point of normal distribution curve, on both sides of mean , 50% of the data falls.

So, % of data of fish which will be longer than 69 cm = 50 % + 34.1 %=84.1%

Now, 84.1% of 310

     $=\frac{84.1}{100}\times 310\\\\=\frac{84.1 \times 31}{10}\\\\=\frac{2607.1}{10}\\\\=260.71$

Approximately,260 or  261 fishes will be longer than 69 cm.    

Answer 2

The answer is 260 fish. Hope this helps.