Andy C. answered • 06/07/18

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Math/Physics Tutor

z = (x - mean)/stddev

1) Prob( 42 < x < 58) = Prob(x<58) - Prob(x<42) = Prob( z < (58-50)/4) - Prob ( z < (42-50)/4)

Prob( z < -2) - Prob( z < -2)

0.9772 - 0.0228 = 0.9554

2) Prob( x<46) = Prob( z < (46-50)/4) = Prob ( z < -1) =0.1587

The third part is done the same way as #1. I will leave it for you to do.