S2 Normal Distribution help

Can anyone please help with the following question, I am struggling to model my answer. Once that bit is done, I can solve the rest.

"A machine cuts a very long plastic tube into short tubes. The length of the short tube is modelled by a normal distribution with mean m and standard deviation 0.25cm. The value of m can be set by adjusting the machine. Find the value of m for which the probability is 0.1 that the length of a short tube, picked at random, is less than 6.50cm."

Thanks!

Reply 1

.raiden.

10

Original post by ninuzu

Can anyone please help with the following question, I am struggling to model my answer. Once that bit is done, I can solve the rest.

"A machine cuts a very long plastic tube into short tubes. The length of the short tube is modelled by a normal distribution with mean m and standard deviation 0.25cm. The value of m can be set by adjusting the machine. Find the value of m for which the probability is 0.1 that the length of a short tube, picked at random, is less than 6.50cm."

Thanks!

P(X<6.50)=0.1 therefore we can find P(Z<... , in terms of m, try it. Drawing a graph may help too.

Reply 2

ninuzu

OP

17

Original post by raiden95

P(X<6.50)=0.1 therefore we can find P(Z<... , in terms of m, try it. Drawing a graph may help too.

I did that, but it doesn't come up with the correct answer. I then thought that I should look for 0.1 in the normal distribution tables, but they start at 0.5..