A machine used to make butter where its masses are normally distributed with mean m and standard deviation s.It is found that 5% from these butters are having mass more than 85g where else 10% are of mass less than 25g. Find the values of m and s. Also find the symmetrical range from mean where 75% of the masses lies.
I have already found the mean and standard deviation here. Mean = 51.3, S.d. = 20.5
(I mainly have problem in the last question. When they say 'symmetrical mean', I'm assuming its 37.5% on either side of the centre of the bell curve? But apart from that, I dont have an idea to solve it. Thank you.)
I assume you have already used the normal tables to work out the distances you need for the mean and standard deviation.
With that done, you're almost there. As I understand it, the question is asking you to provide the values on the edges of the region you correctly described in brackets.
So, look up 0.875 in the normal tables and you find a Z value of 1.15. Multiply this by the standard deviation to get 23.6. This is the distance either side of the mean that you require.
So the range will be (51.3 - 23.6, 51.3 + 23.6) = (27.7,74.9) (You will have to check for rounding errors)