Question

In: Statistics and Probability

using excel and it's functions The table shows a sample of the maximum capacity (maximum number...

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?

Solutions

Expert Solution

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


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