Question

1. for each of the following scenarios, predict the shape of the density curve for the distribution (skewed left, skewed right, uniform, approximately normal). justify your answer. a. height of adult males b. results when asking siri for a random number between 1 and 10. c. annual salary for a major league baseball team d. final exam scores for a really easy class. 2. consider the following density curve. a. which value marks the median? explain. b. which value marks the mean? explain.

Explanation:

Step1: Analyze height of adult males

Many factors like genetics and environment contribute to adult - male height. Most values cluster around the average, with fewer very tall or very short individuals. So, it has an approximately normal distribution.

Step2: Analyze random number from Siri

When asking for a random number between 1 and 10, each number has an equal chance of being selected. So, it has a uniform distribution.

Step3: Analyze annual salary of major - league baseball team

A few star players have extremely high salaries, while most players have relatively lower salaries. This causes the tail on the right - hand side of the distribution to be longer. So, it has a skewed right distribution.

Step4: Analyze final exam scores of an easy class

Most students will score high, with only a few students scoring low. This causes the tail on the left - hand side of the distribution to be longer. So, it has a skewed left distribution.

Step5: Analyze median of given density curve

The median divides the area under the density curve into two equal parts. For a skewed right density curve, the median is less than the mean and is located at the point where the area to the left and right are equal. So, the median is marked by B.

Step6: Analyze mean of given density curve

In a skewed right distribution, the mean is pulled in the direction of the long tail. So, the mean is marked by C.

Answer:

a. Approximately normal. Reason: Heights of adult males cluster around the average with similar numbers of values on either side of the average.
b. Uniform. Reason: Each number between 1 and 10 has an equal probability of being selected.
c. Skewed right. Reason: A few high - salary star players pull the tail to the right.
d. Skewed left. Reason: Most students score high with a few low - scoring students pulling the tail to the left.

1. a. B. Reason: The median divides the area under the density curve into two equal parts.

b. C. Reason: In a skewed right distribution, the mean is pulled towards the long tail.