I have a question this solution that I looked up.  My question is where the bold italicized numbers came from. 1) For this part n=30 So for this the standard deviation is= 10030√10030 So the required probability is: P(||X⎯⎯⎯−273||≤16)=P(−16≤X⎯⎯⎯−273≤16) =P(−1610030√≤X⎯⎯⎯−27310030√≤1610030√) =P(−0.876356≤Z≤0.876356) =P(Z≤0.876356)−P(Z<−0.876356) =0.8096−0.1904=0.6192

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I have a question this solution that I looked up.  My question is where the bold italicized numbers came from.

1) For this part n=30

So for this the standard deviation is= 10030√10030

So the required probability is:

P(||X⎯⎯⎯−273||≤16)=P(−16≤X⎯⎯⎯−273≤16)

=P(−1610030√≤X⎯⎯⎯−27310030√≤1610030√)

=P(−0.876356≤Z≤0.876356)

=P(Z≤0.876356)−P(Z<−0.876356)

=0.8096−0.1904=0.6192

Answer(1): 0.6192

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