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Statistics Normal Distribution HELP

Not sure how to get the answer in the back of the book:

The weights of plums from an orchard have mean 24g and standard deviation 5g. The plums are graded small, medium or large. All plums over 28g are regarded as large and the rest equally divided between small and medium. Find:
(A) the proportion of plums graded large
(
B) the upper limit of the weights of the plums in the small grade

I've got part a to be 0.212. the answer to part b is 22.6g but idk how to get to it
Original post by ppdtg
Not sure how to get the answer in the back of the book:

The weights of plums from an orchard have mean 24g and standard deviation 5g. The plums are graded small, medium or large. All plums over 28g are regarded as large and the rest equally divided between small and medium. Find:
(A) the proportion of plums graded large
(B) the upper limit of the weights of the plums in the small grade

I've got part a to be 0.212. the answer to part b is 22.6g but idk how to get to it


So then 21.2% are large.

Hence 78.8% are small/medium.

Hence 39.4% are small.

So you are looking for kk so that P(0<X<k)=0.394P(0<X<k) = 0.394
Reply 2
Original post by RDKGames
So then 21.2% are large.

Hence 78.8% are small/medium.

Hence 39.4% are small.

So you are looking for kk so that P(0<X<k)=0.394P(0<X<k) = 0.394


thanks for replying!! if i do z^-1(0.394) and put that into z=(x - mean)/sd i get 22.7 for x??? i haven’t rounded off or anything
Original post by ppdtg
thanks for replying!! if i do z^-1(0.394) and put that into z=(x - mean)/sd i get 22.7 for x??? i haven’t rounded off or anything


Error in the textbook. Working to a higher degree of accuracy produced 22.656, which is 22.7 to 3 sig.fig.

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