Upper Limit in normal distribution?

Question

(Iv already solved the a) part with the answer 0.2119, which is correct. The b) part asks for the upper limit, I dont know what an upper limit is in these type of questions. Can any one give me pointers on this? It is a homework question, so hints which lead to the answer as compared to the answer itself would be appreciated, if that is more convenient for you.)

The mass of the fruits from a shop a are normally distributed with mean 24g and standard deviation 5g. Fruits are graded as small, medium and large. All fruits with mass more than 28g are graded as large and the rest are equally shared among the small and medium grades. Estimate:

a) the probability that a fruit is graded as large

b) the upper limit of the mass of a grade small fruits

Answer 1

On the assumption that your answer to (a) is correct, the probability that a fruit is graded as not large is $0,7781$, so the probability that a fruit is graded as small is half of this, which is about $0.39405$.

We want the weight $w$ such that the probability that a fruit has weight $\le w$ is $0.39405$. This $w$ is the boundary between small and medium.

Now you have a standard normal distribution problem. If you need further assistance please leave a message.

Answer 2

Hint: You know that 21.19% of the fruits are large. Half of the rest are small and the other half are medium. Can you tell what proportion of the fruits are small?

Suppose that you can and the answer is $y$. To find the upper limit for small fruits, you need the value of $z$ such that exactly $y$ proportion of the fruits are smaller than $z$. Formally, $F(z)=y$, where $F$ is the cdf of the normal distribution with mean $24$ and standard deviation $5$.