Question

The weight of potato chips in a medium-size bag is stated to be 10 ounces the amount that the packaging machine puts in these bags is believed to have a normal model with mean 10.2 and standard deviation 0.12 ounces. What's the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces?

Answer 1

The probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.

Explanation:

Let X = weight of potato chips in medium size bag.

The random variable X follows a Normal distribution with mean, μ = 10.2 ounces and standard deviation, σ = 0.12 ounces.

A sample of n = 24 bags of chips is selected.

Compute the probability that the mean weight of these 24 bags is less than 10 ounces as follows:

`P(\bar X<10)=P((\bar X-\mu)/(\sigma/√(n))<(10-10.2)/(0.12/√(24)) )\\=P(Z<-8.16)\\=1-P(Z<8.16)\\\approx0`

Thus, the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.