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 ounces and standard deviation 0.12 ounces.
What's the probability that the mean weight of the 3 bags is below the stated amount?
a. 0.069
b. 0.0478
c. 0.9522
d. 0.0019

Answer 1

Answer: d. 0.0019

Step-by-step explanation:

Given : 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 ounces and standard deviation 0.12 ounces.

i.e.  $\mu=10.2$ and $\sigma=0.12$

Let x represents the weight of potato chips in a medium-size bag.

The probability that the mean weight of the 3 bags (i.e. sample size = 3) is below the stated amount will be :-

$P(x<10)=P(\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{10-10.2}{\dfrac{0.12}{\sqrt{3}}})\\\\=P(z<-2.89)=1-P(z<2.89)\ \ [\because P(Z<-z)=1-P(Z<z)]\\\\=1-0.9981=0.0019 \ \ \text{[By using z-value table]}$

Hence, the required probability =0.0019