In: Statistics and Probability
using excel and it's functions
The table shows a sample of the maximum capacity (maximum number of spectators) of sports stadiums. The table does not include horse-racing or motor-racing stadiums.
40,000 | 40,000 | 45,050 | 45,500 | 46,249 | 48,134 |
49,133 | 50,071 | 50,096 | 50,466 | 50,832 | 51,100 |
51,500 | 51,900 | 52,000 | 52,132 | 52,200 | 52,530 |
52,692 | 53,864 | 54,000 | 55,000 | 55,000 | 55,000 |
55,000 | 55,000 | 55,000 | 55,082 | 57,000 | 58,008 |
59,680 | 60,000 | 60,000 | 60,492 | 60,580 | 62,380 |
62,872 | 64,035 | 65,000 | 65,050 | 65,647 | 66,000 |
66,161 | 67,428 | 68,349 | 68,976 | 69,372 | 70,107 |
70,585 | 71,594 | 72,000 | 72,922 | 73,379 | 74,500 |
75,025 | 76,212 | 78,000 | 80,000 | 80,000 | 82,300 |
a) Calculate the sample mean and the sample standard deviation for the maximum capacity of sports stadiums (the data).
b) Let the sample mean approximate μ and the sample standard deviation approximate σ. The distribution of X can then be approximated by X ~ _____(_____,_____).
c) Use the distribution in part e to calculate the probability that the maximum capacity of sports stadiums is less than 67,000 spectators.
d) Determine the cumulative relative frequency that the maximum capacity of sports stadiums is less than 67,000 spectators. Hint: Order the data and count the sports stadiums that have a maximum capacity less than 67,000. Divide by the total number of sports stadiums in the sample.
e) Why aren’t the answers to part f and part g exactly the same?
I have entered the data and calculated the mean and standard deviation of the sample as shown in the below image
Question (a)
I have entered the sample data in cells G2 to G61
The formual for Mean in cell K3 is =AVERAGE(G2:G61)
The mean value as shown in the image is = 60136. 417
The formual for Standard deviation in cell K4 is =STDEV.P(G2:G61)
The standard deviation value as shown in the image is = 10380.502
Be carerful to include = symbol too before the formula in cells K3 and K4
Question (b)
X ~ N (, )
X ~ N(60136.42, 10380.5)
Question (c)
We need to first calcuate the Z-score
Here X = 67,000
= 60136.42
= 10380.5
n = 60
But please mention what is the distribution in part (e) so we can calculate the probability
Question (d)
43 values are less than 67000 out of the total 60 values
So cumulative relative frequency that the maximum capacity of sports stadiums is less than 67,000 spectators
= 43 / 60 = 0.7166 or 71.67%
Question (e)
Please mention part f and part g so i can compare and show you the results or answers