In: Statistics and Probability
A) P(X > 4) + P(X < 2.4)
= P((X - )/ > (4 - )/) + P((X - )/ < (2.4 - )/)
= P(Z > (4 - 3.2)/0.4) + P(Z < (2.4 - 3.2)/0.4)
= P(Z > 2) + P(Z < -2)
= (1 - P(Z < 2)) + P(Z < -2)
= (1 - 0.9772) + 0.0228
= 0.0456
Number of remote control cars would be disqualified = 100 * 0.0456 = 4.56 = 5
B) P(X < x) = 0.9
Or, P((X - )/ < (x - )/) = 0.9
Or, P(Z < (x - 3.2)/0.4) = 0.9
Or, (x - 3.2)/0.4 = 1.28
Or, x = 1.28 * 0.4 + 3.2
Or, x = 3.712