Question

1. A group of fishes chosen randomly were being researched by a zoologist, who found that
the mean tail length of 100 fishes was 10 mm in contrast to a standard reference tail length of
8 mm with a standard deviation of 2 mm. Determine the following:
a. the proportion of fishes with a tail length less than 10 mm.
b. the proportion of fishes with a tail length between 8 and 10mm.
c. the proportion of fishes with a tail length greater than 10 mm.
d. The number of fishes with a tail length greater than 10 mm and the number whose tail
length are less than 10mm.
e. whether there is a significant difference in the mean tail length of the 100 fishes compared
to the standard reference tail length at 95% level of accuracy?

Answer 1

a. 0.5 (50%)
b. 0.8413 (84.13%)
c. 0.1587 (15.87%)
d. 50 fishes with a tail length greater than 10 mm and 50 fishes with a tail length less than 10 mm.
e. Yes, there is a significant difference in the mean tail length of the 100 fishes compared to the standard reference tail length at 95% level of accuracy.