1.The power consumption of a certain brand light bulb have a normal distribution with mean 60 watts and a standard deviation 2 watts. Find the probability that

(a) 3 bulbs selected randomly each has a power consumption exceeding 61 watts.

X ̅~N(60,4/3), P(X ̅>61)= ..........

(b) 3 bulbs selected randomly have a total power consumption exceeding 183 watts.

P(X ̅>61)^3=............

2. X~N(μ,9). Find the smallest sample size required to ensure that the probability that X ̅ is within 0.2 of μ is greater than 0.95.

P(-0.2 < X ̅-μ <0.2) > 0.95

P(-0.05√n < Z < 0.05√n) > 0.95......... and solve it?

Please check for me, thank you.