Question

7. A machine produces memory sticks of varying lengths, distributed uniformly between 3mm and 13 mm. Memory sticks longer than 10 mm do not meet the design criteria and must be scrapped. Calculate the proportion of memory sticks that will be scrapped, which is the probability that memory stickers longer than 10 mm will be scrapped.

Answer 1

The proportion of memory sticks that will be scrapped is 0.3 = 30%.

Explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.

The probability of finding a value of at lower than x is:

`P(X < x) = (x - a)/(b - a)`

The probability of finding a value between c and d is:

`P(c \leq X \leq d) = (d - c)/(b - a)`

The probability of finding a value above x is:

`P(X > x) = (b - x)/(b - a)`

Distributed uniformly between 3mm and 13 mm.

This means that
`a = 3, b = 13`

Calculate the proportion of memory sticks that will be scrapped:

`P(X > 10) = (13 - 10)/(13 - 3) = (3)/(10) = 0.3`

The proportion of memory sticks that will be scrapped is 0.3 = 30%.