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We find the Mean and standard deviation of the maximum seating capacity of stadiums using Minitab
a. Mean = 60143
Standard Deviation = 10462
b.
c. The smooth curve over histogram
d. The histogram is bell shaped, however slightly skewed to the right.
e. X can be more or less approximated by a normal distribution.
X ~ N(60143,10462)
f. P[ X < 67000]
= P[(X - 60143)/10462 < (67000 - 60143)/10462]
= P[ Z < 0.6554] {Z = (X - 60143)/10462 ~ N(0,1)}
= 0.74389 {Values obtained from a standard normal table}
g.
To determine the cumulative relative frequency that maximum capacity of sports stadiums is less than 67000 spectators.
= (Number of stadiums in sample with stadium capacity less than 67000)/ (Total number of stadiums in sample)
= 43/60
= 0.7167
h. The answers in f and g aren't exactly the same because in f we assume normality and fit a normal distribution to the data obtained and then calculate the probability. However in g we just calculate the exact probability based on sample values that are given in the data.
A sample of the maximum capacity of spectators of sports stadiums is included in the table....
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