tricotasu

2020-10-18

Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or skewed? Explain why.
a) The number of speeding tickets each student in the senior class of a college has ever had.
b) Players’ scores (number of strokes) at the U.S. Open golf tournament in a given year.
c) Weights of female babies born in a particular hospital over the course of a year.
d) The length of the average hair on the heads of students in a large class.

likvau

a) Unimodal (near 0) and skewed. Many seniors will have 0 or 1 speeding tickets. Some may have several, and a few may have more than that.
b) Probably unimodal and slightly skewed to the right. It is easier to score 15 strokes over the mean than 15 strokes under the mean.
c) Probably unimodal and symmetric. Weights may be equally likely to be over or under the average.
d) Probably bimodal. Men's and women's distributions may have different modes. It may also be skewed to the right, since it is possible to have very long hair, but hair length can't be negative.

Nick Camelot

a) The number of speeding tickets each student in the senior class of a college has ever had.
The distribution for the number of speeding tickets is expected to be skewed, rather than symmetric. This is because most students are likely to have few or no speeding tickets, resulting in a right-skewed distribution. Only a small proportion of students would have a relatively high number of speeding tickets, causing the tail of the distribution to extend to the right.
b) Players' scores (number of strokes) at the U.S. Open golf tournament in a given year.
The distribution of players' scores at the U.S. Open golf tournament is expected to be unimodal and approximately symmetric. In a golf tournament, the majority of players tend to perform close to the average level, resulting in a bell-shaped distribution. However, there may be a small number of exceptional players who perform significantly better or worse, causing some slight deviations from perfect symmetry.
c) Weights of female babies born in a particular hospital over the course of a year.
The distribution of weights for female babies born in a particular hospital over the course of a year is expected to be unimodal and approximately symmetric. In a large sample, birth weights of female babies typically follow a bell-shaped distribution, with most babies having weights around the average. There may be some slight deviations due to factors such as premature births or other medical conditions, but the overall shape of the distribution is expected to be unimodal and symmetric.
d) The length of the average hair on the heads of students in a large class.
The distribution for the length of average hair on the heads of students in a large class is expected to be unimodal and approximately symmetric. In a large sample, the lengths of hair tend to follow a bell-shaped distribution, with most students having hair lengths around the average. Although there may be some variations due to different hairstyles or hair care practices, the overall distribution is expected to be unimodal and symmetric.

Mr Solver

Step 1:
a)In this case, the distribution of the number of speeding tickets is unlikely to be uniform because different students may have different driving behaviors and may receive varying numbers of tickets. Additionally, it is unlikely to be bimodal because there are no clear groups or categories that would result in two distinct peaks.
The distribution is likely to be unimodal and positively skewed. This is because most students are likely to have zero or a small number of speeding tickets, resulting in a peak at lower values. However, there may be a few students with a significantly higher number of tickets, causing the tail of the distribution to extend towards higher values.
Step 2:
b)The distribution of players' scores at the U.S. Open golf tournament is expected to be unimodal and approximately symmetric. In professional golf tournaments, the majority of players tend to have scores around par or slightly above or below it. The distribution would have a peak around the average score, with a roughly equal number of players scoring above and below the average.
Step 3:
c)The distribution of weights of female babies born in a particular hospital over a year is likely to be unimodal and approximately symmetric. In a healthy population, the weights of female babies tend to cluster around a central value (the mean weight). The distribution would have a peak at the average weight, with a roughly equal number of babies weighing more or less than the average.
Step 4:
d) The distribution of the length of the average hair on the heads of students in a large class could vary depending on cultural norms, personal preferences, and grooming habits. However, assuming no specific external factors, it is reasonable to expect that the distribution would be unimodal and approximately symmetric. Most students would have a hair length around the average value, resulting in a peak around the mean length. The distribution would have a roughly equal number of students with shorter or longer hair lengths.

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