Question

A cereal manufacturer claims that boxes of its cereals weigh 20 oz. on average with a population standard deviation of 0.5 oz. A random sample of 100 boxes is selected. What is the probability that sample mean is between 19.9 and 20.1 oz. Assume that it follows normal distribution.

Answer 1

The central limit theorem for sample means says that if you keep drawing larger and larger samples and calculating their means, the sample means form their own normal distribution (the sampling distribution). The normal distribution has the same mean as the original distribution and a variance that equals the original variance divided by, the sample size.

The random variable has a different z-score associated with it from that of the random variable X.

Given

Lower value = 19.9 oz

Upper value = 20.1 oz

Population mean= = 20 oz

Population standard deviation = = 0.5 oz

Sample size (n) = 100

The probability that the sample mean is between 19.9 and 20.1 oz = area between 19.9 and 20.1 oz

So,

Therefore, the probability that sample mean is between 19.9 and 20.1 oz = 0.95445