What n would be necessary in order to have P 4900 X 5100

What n would be necessary in order to have P (4900 < X < 5100) = 0.99?

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What n would be necessary in order to have P (4900

Solution

Margin of error = (upper limit - lower limit) / 2
= (5100 - 4900) / 2 = 100
Margin of error = z-score for 99% confidence*standard deviation/sqrt n
100 = 2.575*400/sqrt n
sqrt n = 2.575*400/100
n = (2.575*400/100)^2
n = 106
Required size of the sample = 106