(Find Normal Proportions)

The lengths of Atlantic croaker fish are normally distributed with μ = 10 inches and σ = 2 inches.

a) Draw the distribution of fish lengths above the axis, and label the mean (which I believe is μ=10).

b)Gently shade an area on the graph that is equal to the proportion (or percentage) of croaker fish that are between 7 and 15 inches long.

c) Draw the standard normal distribution, label the axis, locate both z-scores on the axis (z7 = -1.5, z15 = 2.5), and shade an area equal to the probability that a randomly chosen croaker fish will be b/t 7 and 15 inches.

We cannot draw distributions on this message board.

b. Z = (score-mean)/SD

Z = (7-10)/2

Z = (15-10)/2

a) To draw the normal distribution of fish lengths, you can start by creating a horizontal axis. Label this axis with the numbers representing the length of the fish in inches. In this case, we know that the mean (μ) is 10 inches. Therefore, mark a point on the axis at 10 inches to represent the mean.

b) To shade the area on the graph representing the proportion of croaker fish between 7 and 15 inches long, we need to determine the z-scores for these lengths. The formula to calculate the z-score is:

z = (x - μ) / σ

Where:
x = the specific length
μ = the mean
σ = the standard deviation

For x = 7:
z7 = (7 - 10) / 2 = -1.5

For x = 15:
z15 = (15 - 10) / 2 = 2.5

Once you have calculated the z-scores, locate these values on the horizontal axis of the graph and mark them accordingly. Then, shade the area between these two z-scores on the graph.

c) To draw the standard normal distribution, you will first need to create a new horizontal axis representing the z-scores. Locate the z-scores (z7 and z15) along this axis and label them accordingly. In this case, z7 is -1.5 and z15 is 2.5.

Next, shade the area on the graph between these two z-scores. This shaded area represents the probability that a randomly chosen croaker fish will have a length between 7 and 15 inches, based on the standard normal distribution.