The Edmonton rush is one of nine teams that play in the national lacrosse league. The weights of the 2013 Edmonton rush players are shown.
Weight in Lbs.
160. 170. 170. 175. 180
185. 188. 190. 190. 190
194. 195. 200. 200. 200
205. 205. 210. 210. 210
210. 215. 245.
A.) Explain why this data is close to being normally distributed.
B.) There were 218 players in the national lacrosse league in 2013. Assuming the mean and standard deviation of the league are same as the mean and standard deviation of the Edmonton rush, predict the number of players that weighed over 231 lbs.
C.) Below what weight should there be approximately 35 national lacrosse league players?
Please help, I have no idea how to do these.
A.) the data is clustered around a central value (mean), with fewer data points towards the edges
B.) from statistical software ...
mean = 195.5 , s.d. = 18.33
231 lbs is 1.94 s.d. above the mean
[(231 - 195.5) / 18.33]
this represents 2.6% of the population
.026 * 218 = 5.67 >>> 6 players
C.) 35 / 218 = .16
this is the fraction of the population below 0.9 s.d. below the mean
195.5 - (0.9 * 18.33) ≅ 179 lbs
A.) Well, let's take a look at the data. The weights of the Edmonton Rush players show a range from 160 lbs to 245 lbs. When we visualize the distribution of the weights in a histogram, we observe that the majority of the data points are clustered around the middle and taper off towards the extremes. This shape resembles a bell curve, which is characteristic of a normal distribution. So, the data is close to being normally distributed because it follows a similar pattern.
B.) To predict the number of players that weighed over 231 lbs, we need to calculate the z-score for 231 lbs using the mean and standard deviation. However, you didn't provide us with the mean or standard deviation values for the Edmonton Rush. Without this information, unfortunately, we cannot give an accurate prediction. But hey, at least we got to use the word "z-score," and it made us feel really smart!
C.) Similarly, to find the weight below which there should be approximately 35 national lacrosse league players, we would again need the mean and standard deviation values. Without them, we can't calculate the exact weight. But, if we're talking approximate numbers, let's say that the average player in the national lacrosse league weighs around 200 lbs with a standard deviation of 20 lbs. Using this rough estimate, we can calculate the z-score corresponding to the desired probability (35 players out of 218), and then convert it back to the weight using the mean and standard deviation.
Overall, it would be best if you could provide the mean and standard deviation values for the Edmonton Rush or the league as a whole so we can give more accurate predictions. Guessing these values is a bit like trying to find a lacrosse ball in a haystack - a challenging task indeed!
A.) The data is close to being normally distributed because the weights of the players are spread out in a bell-shaped curve, with most of the weights clustered around the mean and fewer weights at the extreme ends. Additionally, the data does not have any significant outliers that could skew the distribution.
B.) To predict the number of players that weighed over 231 lbs, we need to calculate the z-score for 231 lbs using the mean and standard deviation of the Edmonton rush. Then, we can use the z-score to find the corresponding percentile, which represents the proportion of players that weigh less than 231 lbs. Finally, we can subtract this proportion from 1 to find the proportion of players that weigh more than 231 lbs. Multiplying this proportion by the total number of players in the league (218) will give us the predicted number of players that weigh over 231 lbs.
C.) To find the weight below which there should be approximately 35 national lacrosse league players, we can use the z-score and inverse norm function. The inverse norm function will give us the z-score corresponding to a given percentile, and we can then use this z-score to calculate the weight using the mean and standard deviation of the Edmonton rush.
A) To understand why the data is close to being normally distributed, we need to examine the characteristics of a normal distribution. A normal distribution, also known as a bell curve, is a symmetric probability distribution where most of the data falls near the mean, and the data points farther away from the mean become less frequent. It is characterized by its shape, center, and spread.
Looking at the weights of the Edmonton Rush players, we can see that the data points, when plotted on a histogram or a frequency distribution, appear to form a bell-shaped curve. The majority of the data falls within the range of 170 to 210 pounds, with 190 pounds being the most common weight. The data tapers off as you move farther away from the mean, with fewer players having weights outside the range of 160 to 240 pounds.
B) To predict the number of players that weighed over 231 pounds, we can use the concept of standard deviation. The standard deviation measures the spread or variability of the data points around the mean. Assuming the mean and standard deviation of the league are the same as those of the Edmonton Rush, we can calculate the number of players weighing over 231 pounds.
First, let's calculate the mean and standard deviation of the given data:
Mean (μ) = (Sum of all weights) / (Number of players)
Standard Deviation (σ) = Square Root of [(Sum of ((each weight - mean)^2)) / (Number of players)]
Using the provided weights, we can calculate the mean and standard deviation.
Mean (μ) = (160 + 170 + 170 + 175 + 180 + 185 + 188 + 190 + 190 + 190 + 194 + 195 + 200 + 200 + 200 + 205 + 205 + 210 + 210 + 210 + 215 + 245) / 22 ≈ 194.6 pounds
Standard Deviation (σ) = Square Root[( (160 - 194.6)^2 + (170 - 194.6)^2 + ... + (245 - 194.6)^2) / 22] ≈ 23.54 pounds
Now, we can use the Z-score formula to find the number of players weighing over 231 pounds:
Z-score = (Weight - Mean) / Standard Deviation
Z-score = (231 - 194.6) / 23.54 ≈ 1.53
Using a standard normal distribution table or calculator, we can find the proportion of data beyond the Z-score of 1.53. This proportion represents the approximate percentage of players weighing above 231 pounds in the league.
C) To determine the weight below which there should be approximately 35 national lacrosse league players, we need to calculate the corresponding Z-score and then convert it back to the weight using the mean and standard deviation.
First, let's find the Z-score using the formula:
Z-score = (Weight - Mean) / Standard Deviation
To find the weight corresponding to a Z-score, we rearrange the formula:
Weight = (Z-score * Standard Deviation) + Mean
Given that we are looking for the weight below which there should be approximately 35 players, we can calculate the Z-score corresponding to this percentile using a standard normal distribution table or calculator. Once we have the Z-score, we can use the formula to find the weight.
This process of finding Z-scores and converting them back to weights is how we can estimate the number of players in a particular weight range or percentile.