One side of a square is measured to the nearest centimetre and this measurement is multiplied by 4 to estimate the perimeter of the square. The random variable, \(W \mathrm {~cm}\), represents the estimated perimeter of the square minus the true perimeter of the square.
\(W\) is uniformly distributed over the interval \([ a , b ]\)
Explain why \(a = - 2\) and \(b = 2\)
The standard deviation of \(W\) is \(\sigma\)
Find \(\sigma\)
Find the probability that the estimated perimeter of the square is within \(\sigma\) of the true perimeter of the square.
One side of each of 100 squares are now measured. Using a suitable approximation,
find the probability that \(W\) is greater than 1.9 for at least 5 of these squares.