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Hi sir,
question: XYZ manufactures chemicals used in industry. It sells its chemical XX in 500-liter containers. The containers are filled automatically by specially designed equipment. Though testing a sample of
filled containers it is found that the quantities follow a normal distribution and have a mean of
500 litres. Recent tests showed that 7% of containers contained more than 510 litres.
What is the standard deviation of the distribution?I did some calculations like 0.5-0.07 = 0.43 from that I get a z score. But I am stuck after that when I saw the answer I don’t understand where did they get Z= 1.48?
thanks in advance
Hi there I can tell you the answer for this It is quite easy.
Let me make you understand.
In this question it is asking about standard deviation okay
So first of all you had exactly done right till this step that you found the answer 0.43 or 0.4300
After this you have to Find this value or nearest to this value in the Distribution table ( not at the side of column or row ) but in the middle of the table, exact value is not available (0.4300) so you have to take this value 0.4306 instead of 0.4300.
Now see the Row and column in which this value is present I mean 0.4306, You will find 1.4 in row and 0.08 in column which means 1.48 and this is required and after that you will get your standard deviation easily.
That is Standard Deviation 6.76.
If you have any question let me ask.If you don’t mind I’ll ask one more question but for another one. If you know how to deal with that. I need an easy explanation
A business has analyzed its customer collection data and has found that a customer takes 37 days to pay on average with a standard deviation of 4 days.
Assuming the data follows a normal distribution, what is the probability that a customer will take longer than 47 days to pay?
My answer: 49.38%
Calculations:
z= 47-37/4 = 2.5
from the table 2.5= 0.4938 which means 49.38%
But for some reason, the answer is 0.62%
can you tell me why they subtracted 49.38% from 50%?
Let me make you understand
z=47-37/4 = 2.5
okay then you have to see 2.5 in row and 00 column you will find 0.4938
Than from 0.5 you have to subtract this amount
I mean 0.5-0.4938 and then multiply by 100 to get answer in percentage’
you will definitely find 0.62 %
Okay but I want to know the reason why we subtracting ? What I don’t understood properly? I am not about calculations… I am more concerned about concept behind these calculations.
When we have to find probability we must deduct the amount which we find from table from 0.5.
It is mandatory and remember this for your whole life.
I don’t know why we do this but to find probability it is necessary.syedfahad1: Please do not answer questions in this forum because it is the Ask the Tutor Forum and you are not the tutor. (But please do help students in the other Paper MA forum 🙂 )
Sakuna: seyedfahads answers are correct. The reason for subtracting from 0.5 is that the distributions symmetrical about the mean, so 0.5 are above the mean and 0.5 are below the mean.
Have you watched my free lectures on this?
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