Answer:
The probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.
Step-by-step 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:
[tex]P(\bar X<10)=P(\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{10-10.2}{0.12/\sqrt{24}} )\\=P(Z<-8.16)\\=1-P(Z<8.16)\\\approx0[/tex]
Thus, the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.
