Question

The lengths in meters of pieces of scrap wood found on a building site are uniformly distributed between 0.0 and 2.5.

What is the probability that at least 20 out of 25 pieces of scrap wood are longer than 1 meter?

Answer 1

can someone please walk me through how to do this? i know that im suppose to use binomial distrbution with it but i dont know how

Answer 2

What is the probability to choose one piece longer than 1?

Answer 3

Probability of 1 meter or higher = 0.6 = (2.5 - 1.0) / (2.5 - 0.0)
but the thing is they dont give me that info so im not sure

Answer 4

Great
Let us call it p=.6 the probability of success

Answer 5

What is the probability of failure q?

Answer 6

q=1-p=.4

Answer 7

You should compute
\[
{25 \choose 20} (.6)^{20} \, (.4)^5
\]

Answer 8

Which is about
0.0198914
The answer is close to 2 %

Answer 9

yes, but WHY is it 0.6

Answer 10

Because of uniform distribution between 0 and 2.5
to get more than 1, you have to be in the interval [1,2.5] which has length of 1.5
\[
p= \frac {1.5}{2.5}=.6
\]

Answer 11

Good approach. I agree that the chances of picking a piece of wood that is at least 1 meter long is 0.6. You pick 25 samples and want to know the prob. that 20, 21, 22, 23, 24 or 25 of them are at least 1 meter long.

How would you calculate that probability? If you use the binomal probability distribution function, n would be 25, p would be 0.6. You'd have to calculate the probability of obtaining 20 "successes," 21, 22, 23, 24 or 25 and add these probs. together. Or, you could use the binomial probability "cumulative probability density function" on a TI calcuator.