Q6 / Ex. 15B

[Multi25]

Does anyone know how to do Question 6 from 15B of Cambridge Spesh Maths?

[jamonwindeyer]

Hey! You might want to post a pic, you're more likely to get an answer that way

[Multi25]

Oh, sorry! Tried that and there was an error saying the image file was too big to attach (working off my tablet you see...)...

It's all G, I'll just type it up:

Suppose that the weights of people are normally distributed with a mean of 82 kg and a standard deviation of 9 kg. What is the maximum number of people who can get into an elevator which has a weight limit of 680 kg, if we want to be at least 99% sure that the elevator does not exceed capacity.

I tried using the methods in the book but I kept getting slightly different answers. Also for the next two questions which are similar the answers they provide can only be attained by using the rule: Var(aX) = aVar(X)  as opposed to Var(aX) = (a^2)Var(X)...  : (

[wyzard]

Oh, sorry! Tried that and there was an error saying the image file was too big to attach (working off my tablet you see...)...

It's all G, I'll just type it up:

Suppose that the weights of people are normally distributed with a mean of 82 kg and a standard deviation of 9 kg. What is the maximum number of people who can get into an elevator which has a weight limit of 680 kg, if we want to be at least 99% sure that the elevator does not exceed capacity.

I tried using the methods in the book but I kept getting slightly different answers. Also for the next two questions which are similar the answers they provide can only be attained by using the rule: Var(aX) = aVar(X)  as opposed to Var(aX) = (a^2)Var(X)...  : (

For a normal distribution, for the sum of multiple random variables, their mean and variance will add up and it remains to be a normal distribution. This can be shown by using convolution integral, and the mathematics can get pretty messy, took me 3 pages of algebra to show that 

So for this case, add up their mean and variances, until you hit the maximum value where there's 99% chance that the total weight is less than 680kg.

[Sp123]

I would recommend you go watch this youtube video beginning 14.50 minutes https://www.youtube.com/watch?v=3p22J6PAInE. I had the same problem and I watched this and figured it out. Just apply the same concept.

I got Pr(Y<680) = 0.99
        Pr(Z<(680-82n)/(9sqrt n))=0.99

got n=7.59 and u round it down to 7 people because if you round it up, it would exceed 680.

[Multi25]

Thanks guys!

U just made my day! I can finally sleep now...  ; )