There's a set of 8 bags with the following weights in grams given:
1013, 997, 1013, 1013, 1004, 985, 991, 997
The mean is 1001.625, unbiased standard deviation is 10.86.
I have the following question on an exam paper:
Assuming the standard deviation is 10 and the bags have a mean weight of 1kg (1000g),
calculate the probability that five randomly selected bags together weigh more than
4.99kg.
Could someone please help me calculate this? How do I get from the weight of the bags, mean and standard deviation to the probability that five random ones weight more than something?
Best Answer
You need to know the distribution the bags are sampled from. If it is assumed to be normal with mean 1000 g and standard deviation 10 g then the sum of 5000 g and variance 500 g or standard deviation 10 √5. Then Z= (X-5000)/(10 √5) has a standard normal and the probability
P[X>a]=P[Z>(a-5000)/(10 √5)] which can be obtained from the table of the standard normal distribution.