Statistics Help on Probability

I am struggling on a Probabilty question about paint being applied to cars.

The table needed is as follows:

_____________Mean ____Standard Deviation
Primer_________3.7__________1.2
Undercoat______3.9__________0.9
Top Coat_______4.0__________0.75

(I hope it is easy to follow)

My questions about this are:

1. How do I find the total amount of paint used on average on each car?

2. What percentage of cars will use less than 3 litres of Top Coat?

3. The probability that a car, selected at random, will use between 2.3 litres and 4.5 litres of undercoat?

4. What percentage of cars will use more than 3.2 litres of Primer?

5. If a car receives less than 2 litres of top coat there is a quality issue about this paintwork. The company requires that no more than 2% of the cars should present this problem. The amount of paint dispensed can be adjusted. Determine a new mean such that this quality requirement will just be satisfied. Use an appropriate standard deviation from the table.

We can assume that they follow a Normal Distribution

I've been stuck on this for the past 2 days, I really cannot get my head around it for some reason.

Thanks for any help.

(edited 11 years ago)

Reply 1

ghostwalker

Original post by D556mm

The average total amount of paint use is the sum of the average amount of primer, the average amount of undercoat,...

Thanks for any help.

For the remainder of your questions we need to know the distribution of the amounts. Can we assume they're normally distributed?

Reply 2

D556mm

Original post by ghostwalker

The average total amount of paint use is the sum of the average amount of primer, the average amount of undercoat,...

For the remainder of your questions we need to know the distribution of the amounts. Can we assume they're normally distributed?

Yes, we can assume they are Normally Distributed. I forgot to edit that in.

Reply 3

ghostwalker

Original post by D556mm

Yes, we can assume they are Normally Distributed. I forgot to edit that in.

So, for question 2, the top coat is distributed

N(4,0.75^2)

and you're interested in the probability that the amount of top coat is <=3.

Can you work that out? And if not, say what you're stuck with.

Reply 4

D556mm

Original post by ghostwalker

So, for question 2, the top coat is distributed

N(4,0.75^2)

and you're interested in the probability that the amount of top coat is <=3.

Can you work that out? And if not, say what you're stuck with.

I standarized it and got a percentage of 90.82% then subtracted from 100% to then get 9.18% (seemed about right since the mean is 4)

PS. I last did Stats 2 years ago for my 1st year at college and haven't done it since so I'm a bit rusty

(edited 11 years ago)

Reply 5

ghostwalker

Original post by D556mm

Well, you seem to have remembered it.

One point, depending on the accuracy of the tables/software you're using.
A standard deviation of 1.333 gives 90.87% (in my tables). 1.33 gives 90.82%, as you had.

Edit: Going to try and see the comet now.

(edited 11 years ago)

Reply 6

D556mm

Original post by ghostwalker

Even in college, I could never remember when to subtract 1 or leave it as it is from the probabilities given in the table

Reply 7

ghostwalker

Original post by D556mm

Even in college, I could never remember when to subtract 1 or leave it as it is from the probabilities given in the table

You do need to subtract it from 1, or 100% in this case, as you did.

A quick sketch of the normal curve and plotting the sd you're interested in may help.

Couldn't see the comet :sad:

Reply 8

D556mm

Original post by ghostwalker

You do need to subtract it from 1, or 100% in this case, as you did.

A quick sketch of the normal curve and plotting the sd you're interested in may help.

Couldn't see the comet :sad: