Most computer random number generators (at least initially--we can build others based on this) give random numbers uniformly distributed between 0 and 1. That is, any number between 0 and 1 is equally likely to occur. Because the area under the curve is equal to 1, each tenth occurs 10% of the time, or 0.1. What proportion of the time should our random number generator give us a value less than 0.3 or larger than 0.8?

a) 30% of the time we will have numbers smaller than 0.3

a) 20% of the time we will have numbers bigger than 0.3

Explanation:

Since each number is equally likely to occur → 10% of possible values (lets say from 0 until 0.1 is 10% of the range between 0 and 1) will happen 10% of the time

thus

a) less than 0.3 → all numbers between 0 and 0.3 → is the 30% of all the possible values (from 0 to 1). This can be calculated as

proportion of the Population = range of numbers between 0 and 0.3 / maximum range (all possible numbers)

proportion of the Population = (0.3 - 0) / (1-0) = 0.3 = 30%

since 30% of possible values will happen 30% of the time → all numbers between 0 and 0.3 will happen 30% of the time

b) larger than 0.8 → all numbers between 0.8 and 1

proportion of the Population = range of numbers between 0.8 and 1 / maximum range (all possible numbers)

proportion of the Population = (1 - 0.8) / (1-0) = 0.2 = 20%

since 20% of possible values will happen 20% of the time → all numbers between 0.8 and 1 will happen 20% of the time