Question

The weight of corn chips dispensed into a 14-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 14.5 ounces and a standard deviation of 0.2 ounce. suppose 100 bags of chips are randomly selected. find the probability that the mean weight of these 100 bags exceeds 14.6 ounces.

Answer 1

The probability that a normally distributed dataset with a mean, μ, and statndard deviation, σ, exceeds a value x, is given by

$P(X\ \textgreater \ x)=1-P(X\ \textless \ x)=1-P\left(z\ \textless \ \frac{x-\mu}{\frac{\sigma}{\sqrt{n}}} \right)$

Given that the weight of corn chips dispensed into a 14-ounce bag by the dispensing machine is a normal distribution with a mean of 14.5 ounces and a standard deviation of 0.2 ounce.

If 100 bags of chips are randomly selected the probability that the mean weight of these 100 bags exceeds 14.6 ounces is given by

$P(X\ \textgreater \ 14.6)=1-P\left(z\ \textless \ \frac{14.6-14.5}{\frac{0.2}{\sqrt{100}}} \right) \\ \\ =1-P\left(z\ \textless \ \frac{0.1}{\frac{0.2}{10}} \right)=1-P\left(z\ \textless \ \frac{0.1}{0.02} \right) \\ \\ =1-P(z\ \textless \ 5)=1-1=0$

Therefore, the probability that the mean weight of these 100 bags exceeds 14.6 ounces is 0.