Question

Suppose the weight of a certain brand of bolts has the mean value 2 gram and the standard deviation 0.1 gram. Estimate the probability that 150 of these bolts weigh more than 304 grams.

a) Use the Law of Large numbers.

b) Use the Central Limit Theorem.

Compare the results.

Answer 1

average weight of sample = 304/150 = 2.0267

we want o find probability that average weight >= 2.0267

a.

mean of total weight = 2*150 = 300 gram

SD of sample total = 150*SD = 150*0.1 = 15 gram

P(sample total >= 304) :

b.

SD of sample = SD/(n^0.5)

= 0.1/(150^0.5)

= 0.0082

answer : 0.0006