Suppose an experiment involves rolling a fair die 720 times. Find the mean of the number of times a number less than 2 is rolled
only one possibility of rolling a number less than 2, namely the number 1
prob(one) = 1/6
number of times this happens rolling 720 times
= (1/6)(720) = 120
To find the mean, we need to calculate the average number of times a number less than 2 is rolled out of the 720 rolls.
Step 1: Identify the probability of rolling a number less than 2
Since there is only 1 face on the die that is less than 2 (which is 1), the probability of rolling a number less than 2 is 1/6.
Step 2: Calculate the expected number of times a number less than 2 is rolled
To find the expected value (mean), multiply the probability by the total number of rolls:
Expected value = Probability * Total number of rolls
Expected value = (1/6) * 720
Expected value = 120
Therefore, the mean (expected value) of the number of times a number less than 2 is rolled in 720 rolls is 120.