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Homework Help: Please Help Me!
Posted by Courtney B. on Monday, June 20, 2016 at 4:20pm.
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?
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
To answer each part of the question:
A.) To determine if this data is close to being normally distributed, we need to examine the shape of the distribution. One way to do this is by creating a histogram of the weights. A histogram is a graph that displays the frequency or count of each data value within certain intervals or bins.
Here's how you can create a histogram using this data:
1. Arrange the weights in ascending order:
160, 170, 170, 175, 180, 185, 188, 190, 190, 190, 194, 195, 200, 200, 200, 205, 205, 210, 210, 210, 210, 215, 245.
2. Determine the number of bins you want to divide the data into. For this example, let's use 5 bins.
3. Calculate the width of each bin by finding the range of the data divided by the number of bins: (245 - 160) / 5 = 17.
4. Create the bins:
- Bin 1: 160 - 176 (exclusive)
- Bin 2: 176 - 192 (exclusive)
- Bin 3: 192 - 208 (exclusive)
- Bin 4: 208 - 224 (exclusive)
- Bin 5: 224 - 240 (inclusive)
5. Count the frequency of each weight and place it in the appropriate bin.
6. Draw a bar graph, where the height of each bar represents the frequency(count) in each bin.
Once you have created the histogram, you can visually analyze whether the distribution of weights is close to being normally distributed. Look for a bell-shaped curve with a symmetrical pattern.
B.) To predict the number of players that weighed over 231 lbs, we can use the concept of z-scores. A z-score represents the number of standard deviations a data point is away from the mean.
To calculate the z-score:
1. Calculate the mean and standard deviation of the weights using the given data.
- Mean (μ) = (sum of all weights) / (number of players)
- Standard Deviation (σ) = the square root of the variance, where variance = [(each weight - mean) squared] / (number of players)
2. Calculate the z-score using the formula: z = (x - μ) / σ
- x is the value you want to find the z-score for (in this case, 231 lbs)
3. Use a z-score table or calculator to find the corresponding probability or percentile value for the z-score obtained.
4. Multiply the probability by the total number of players in the league (218) to get an estimate of the number of players weighing over 231 lbs.
C.) To determine the weight below which there should be approximately 35 national lacrosse league players, you can use the concept of percentiles.
To find the weight below which there are approximately 35 players:
1. Sort the weights in ascending order.
2. Calculate the percentile rank for 35 players using the formula: PR = (number of players below desired weight / total number of players) * 100
3. Find the weight corresponding to the calculated percentile rank, which should give you an approximate weight below which there are approximately 35 players in the league.