Weight of a bag of crisps follows a normal law. Should calculating the probability that one weighs < 140 g take care if bags are in samples? I'm stuck at an exercise question.
A bag of crisps has a weight that follows $X \sim N(m=150\ \rm g, \sigma=20\ \rm g)$
we are taking samples of 15 bags of crisps
whose have for mean weight $\overline{X} \sim N(m=150\ \rm g, \sigma=5.164\ \rm g)$
The question I am asked by a book is:
What's the probability that a bag of crisps weighs less than 140 g?
What shall I understand and do here?

*

*Draw the $N(m=150\ \rm g, \sigma=20\ \rm g)$, the weight of a bag of crisps whether it is in a sample or not, on a paper or calculate when $X \leq 140\ \rm g$?


*Shall I take care that the question could be understood as:



*

*What's the probability that one (and only one) bag of crisps weighs less than 140 g?
Then, I should take in account that we are considering a sample of 15 bags of crisps, meaning that I am doing 15 draws, and I am expecting to follow an Binomial law giving us one success only?


*or the opposite: up to all bags could weigh less than 140 g, and I would be looking for one success or more?


*Something else? I don't think $\overline{X} \sim N(m=150\ \rm g, \sigma=5.164\ \rm g)$ could be involved, here. But maybe a proportion?

The expected result is 0.3086 says my book. But I'm bit lost, you see.
Can you help me?

You are correct that the sample has nothing to do with this question.
The easy way to answer the question is to find a normal distribution calculator like this: https://keisan.casio.com/exec/system/1180573188
There you can plug in the X (140 g) along with information of the distribution (150 g, 20 g) and it will tell you that the lower cumulative P (The probability of finding a bag 140 g or lower) is about 0.309.

The trickier way (but easier without specifically a normal distribution calculator) is to "standardise" the measurement you have. You do this by first subtracting the mean and then dividing by the standard deviation. So to standardise your 140 g you would compute (140-150)/20 = -0.5.
Then you can look up this standardised value in a z table like this: https://www.ztable.net/
It will also tell you the probability is 0.309.
