Walleye is a common game fish. Adult walleye have a length with a mean of 44 cm and a standard deviation of 4 cm and the distribution of lengths is approximately Normal. What fraction of walleye are longer than 52 cm in length?
52 is 2 std above the mean of 44.
So, look up Z=2 in your table, and subtract that from 1.
Or, mosey on over to
http://davidmlane.com/hyperstat/z_table.html
and enter 2 in the "Above" box and it will calculate the Z value and show the tail of the graph.
To find the fraction of walleye that are longer than 52 cm in length, we can use the properties of the normal distribution.
Step 1: Standardize the value
First, we need to standardize the value of 52 cm using the formula: z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, x = 52 cm, μ = 44 cm, and σ = 4 cm.
Standardizing, we get: z = (52 - 44) / 4 = 2.
Step 2: Find the area under the curve
Next, we need to find the area under the normal curve to the right of z = 2. This represents the fraction of walleye that are longer than 52 cm.
Using a standard normal distribution table or a statistical calculator, we can find that the area to the right of z = 2 is approximately 0.0228.
Therefore, the fraction of walleye that are longer than 52 cm in length is approximately 0.0228, or 2.28%.
To find the fraction of walleye that are longer than 52 cm in length, we need to calculate the area under the normal distribution curve to the right of 52 cm. We can then convert this area to a fraction.
Let's calculate the z-score for the length of 52 cm using the formula:
z = (x - mean) / standard deviation
where x is the length of 52 cm, mean is the mean length of the walleye (44 cm), and standard deviation is the standard deviation of the lengths (4 cm).
z = (52 - 44) / 4
z = 8 / 4
z = 2
The z-score of 2 tells us how many standard deviations away from the mean the length of 52 cm is.
Now, we can use a standard normal distribution table or a calculator to find the area to the right of z = 2. This area represents the fraction of walleye that are longer than 52 cm.
Looking up the value in a standard normal distribution table, we find that the area to the right of z = 2 is approximately 0.0228.
Therefore, approximately 0.0228 (or about 2.28%) of walleye are longer than 52 cm in length.