Question

Melons are sold in three sizes: small, medium and large. The weights follow a normal distribution
with mean 450 grams and standard deviation 120 grams. Melons weighing less than 350 grams are
classified as small.
(i) Find the proportion of melons which are classified as small.
(ii) The rest of the melons are divided in equal proportions between medium and large. Find the
weight above which melons are classified as large.

Answer 1

I've gotten the first answer as 20.2%

Answer 2

what r the choices u can choose from

Answer 3

These types of questions don't normally have choices :)

Answer 4

@dillon754 wtf you're crapping ?

Answer 5

what

Answer 6

Once you hit Algebra I, you stop having multiple choice :)

Answer 7

This is statistics.

Answer 8

that sucks

Answer 9

Get lost if you're not helping here. Thanks.

Answer 10

im not good at algebra im really sorry

Answer 11

For the first one, it's \(\large 20.33%\). Please be nice :)

Answer 12

For the second one, it's 480 grams.

Answer 13

and how do we get to 480 as a solution?

Answer 14

\(\huge1 - 0.2033 = 0.7967 \)
\(\huge \frac{0.7967}{2} = 0.39835 \)

Answer 15

So the proportion of large melons would be 0.39835.

Answer 16

seems like a fair approach :)

Answer 17

im really sorry

Answer 18

The x value which separates the top 0.39835 melons from the rest is about \(+0.25\). The weight of a large melon = y = the mean \(+ (z \times standard~deviation)\)

Answer 19

I don't understand . :(

Answer 20

So you have \(450+(0.25\times 120)=?\)

Answer 21

What don't you understand? :)

Answer 22

Slow down. I don't get your second last comment.

Answer 23

What do you mean by the x value separates and all.

Answer 24

I meant x, not z, sorry. The proportion of the melons that are large compared to those that are medium is 39.835%. When we average in the difference between large and small, we get about 25%.

Answer 25

Since the average weight of a melon is 450 grams, we multiply 0.25 and the standard deviation (120) together and add the product to 450, which gives us 480 grams as the size of the smallest large melon :)

Answer 26

I still don't get it, :(

Answer 27

How did you get 25%?

Answer 28

You just freaking copied whatever the yahoo answer said.

Answer 29

25% is the average differentiation between large and small, and large and medium. Pardon me?

Answer 30

you found the percentage of small, the information tells us that med and large split the difference.

Answer 31

small + (1-small)/2 is the dividing line between med and large

Answer 32

assuming you want a left tail that is

Answer 33

when we know the percentage that is the dividing line, we can use an inverse normal function to determine a z score, and thereby find the weight that is associated with it

Answer 34

How to get. 0.25??

Answer 35

Is it possible to illustrate the graph for me?

Answer 36

i cant draw a the moment, just have a keyboard

the percentages are divided up along the distribution like this:

k% n% n%
|-------------|---------------|---------------|
small med large

such that k% + n% + n% = 100%, agreed?

Answer 37

Yes!

Answer 38

we know the zscore for small is: (350-450)/120 = -0.8333, which we can table or calculator as; 20.23 % agreed?

Answer 39

Yup.

Answer 40

so:

20.23% + 2n% = 100%

n% = (79.77%)/2 = 39.885%

this tells us the split between med and large is 20.23% + 39.885% = 60.115%

agreed?

Answer 41

Yes

Answer 42

now, we need to work an inverse normal function, it takes a percentage and gives us a zscore. we can either do this by a table finding the closest field value to .60115 or a calculator that has an invnorm function.

the wolf gives us: invnorm(.60115) = 0.256 for the associated zscore.

Answer 43

we can now use this inn the zscore formula to find x:\[z=\frac{x-mean}{sd}\]
solving for x we get:
\[mean + z(sd)=x\]
using our values we have:\[450+0.256(120) = x\]which is the dividing line between med and large

Answer 44

Thanks so much. I finally understand. :)