Question

AP Stats: Consider the following information about three populations:

Red Salmon:

mean = 12 lbs. standard deviation = 3 lbs

% of salmon > 18 lbs = 20.0%

% of salmon < 6 lbs = 10.0%

Blue Salmon:

mean = 15 lbs. standard deviation = 5 lbs

% of salmon > 25 lbs = 2.5%

% of salmon < 10 lbs = 16.0%

White Salmon

mean = 18 lbs. standard deviation = 4 lbs

% of salmon > 18 lbs = 30.0%

% of salmon < 10 lbs. = 30.0%

Answer 1

Which of the following populations may be normally distributed?

a) Red and White Salmon

b) Blue Salmon only

c) Red Salmon only

d) White Salmon only

e) None of the above

Answer 2

My guess would be E. If I did my math correctly, none of these match up with the Empirical Rule. Also, I think the White Salmon mean might be a typo, and the instructor meant to put 14 lbs, instead of 18 lbs.

Answer 3

Why did you reject the blue salmon as a possibility?

Answer 4

Here is the empirical rule in graphical form:

Answer 5

Oh, okay I think I see what you're getting at. I completely misunderstood the choice
Blue Salmon:

mean = 15 lbs. standard deviation = 5 lbs

% of salmon > 25 lbs = 2.5%

% of salmon < 10 lbs = 16.0%

the % of salmon > 25 lbs would be around 2.5% because 25 lbs is 2 deviations away from the mean, and just looking at the right half of the graph, that would mean anything 25 lbs and under is about 47.5%, which would leave about 2.5% left over, right?

Answer 6

I hope I said that correctly. I'm still a bit confused on how % of salmon < 10 lbs = 16.0% meets the requirements as well, though. Could you explain that part to me please?

Answer 7

Looking at the graph of the normalized standard deviation, 50% of the data lies to the left of the mean at point zero. Also 68/2 = 34% of the data lies between the mean and -1 standard deviation. Therefore 50 - 34 = 16% of the data lies to the left of -1 standard deviation.

Answer 8

Oh okay, thank you so much for clarifying that! I really appreciate it

Answer 9

You're welcome :)