In: Statistics and Probability
The inside diameter of a piston ring is normally distributed with a mean of 10 cm and a standard deviation of 0.04 cm.
a) P(X < 10.075)
= P((X - )/ < (10.075 - )/)
= P(Z < (10.075 - 10)/0.04)
= P(Z < 1.88)
= 0.9699
b) P(9.94 < X < 10.045)
= P((9.94 - )/ < (X - )/ < (10.045 - )/)
= P((9.94 - 10)/0.04 < Z < (10.045 - 10)/0.04)
= P(-1.5 < Z < 1.13)
= P(Z < 1.13) - P(Z < -1.5)
= 0.8708 - 0.0668
= 0.8040
c) P(X > 10.066)
= P((X - )/ > (10.066 - )/)
= P(Z > (10.066 - 10)/0.04)
= P(Z > 1.65)
= 1 - P(Z < 1.65)
= 1 - 0.9505
= 0.0495
d) n = 5
p = 0.0495
It is a binomial distribution.
P(X = x) = nCx * px * (1 - p)n - x
P(X = 4) = 5C4 * (0.0495)^4 * (1 - 0.0495)^1 = 0.00003
e) Probability = 14C2 * (0.0495)^2 * (1 - 0.0495)^12 * 0.0495 = 0.0060