How do I calculate mean of a second variable with just just the mean and standard deviation of the first? (AP stats)

Question

I don know really how to explain but I am currently working on some ap stats homework and I am incredibly confused. I will post the question below.

A certain box of cereal is labeled as 32 ounces, but boxes actually contain, on average, 33.1 ounces of cereal with a standard deviation of 0.4 ounces. The distribution of weights is approximately Normal. Let X represent the weight of cereal in a randomly selected box. a) Let B represent the extra cereal contained in a box of cereal (i.e. the cereal above the advertised 32 ounces). Find the mean and standard deviation of B. b) Find the P(B > 2).

Honestly, this is the easiest question on the assignment and I am already lost so I don't have a great feeling about the rest lol.

Answer 1

I've taken AP statistics so I can help you out.

As mentioned in the comments, the extra cereal is $B=X-32$ cuz you have X cereal and you find the extra. $B=X-32\sim N(1.1,.4^2)$ cuz you just shift it. The squiggly means it follows a normal distribution with mean 1.1 and variance .4^2.

So the answer for part a is 1.1 and .4, because standard deviation is the square root of variance.

For part b, you need to calculate a zscore. The zscore is $z=\displaystyle \frac {2-1.1}{.4}$. Calculate this and see what percent of the normal distribution is to the right of it. You will likely need to find the probability to the left of it and subtract that from $1$ by using a table provided in your book or elsewhere.

Answer 2

Read @Stacker's (+1) Answer first:

You have $B \sim \mathsf{Norm}(\mu=1.1, \sigma = 0.4).$ Then $P(B > 2) = 1 - P(B \le 2).$

From R statistical software, where pnorm is a normal CDF, using the standard deviation:

1 - pnorm(2, 1.1, .4)
[1] 0.01222447

According to @Stacker's advice for printed normal tables, you will not get that many digits of accuracy, but the answer from R will give you a clue whether you got the right numerical answer from the table. Depending on the format 0f your table, you might get $1 - 0.9878.$