Question

Electronic sensors of a certain type fail when they become too hot. The temperature at which a randomly chosen sensors fails is T Centigrade, where T is normally distributed with mean y = 94.5 and standard deviation o = 5.7. The manufacturers wish to quote a safe operating temperature at which 97% of the sensors will work. What temperature should they quote? 60.71 70.34 83.78 85.14 O O 90.12

Answer 1

P(Z > z)= 0.97 1-P(Z = z)= 0.97 P(Z <z)=0.03 x-u, X-94.5 = P(ZS-1.88 Po 5.7 ) X-94.5 -1.88 5.7 X-94.5=-1.88(5.7) X-94.5=-10.716 X = -10.716+94.5 X = 83.78 The temperature should they quote is 83.78.