In the 2001 population census, information was collected about the number of people in each household, which is denoted by X. It is given that P(X=1) = 0.25, P(X=2) = 0.32, P(X=3) = 0.18, P(X=4) = 0.15, P(X=5) = 0.07, P(X=6) = 0.02 and P(X\geq 7) = 0.01. If R is the probability that there are at most 4 people in the household, what is the value of 100R?
To find the probability that there are at most 4 people in the household, we need to calculate the cumulative probability up to X = 4.
Given that P(X=1) = 0.25, P(X=2) = 0.32, P(X=3) = 0.18, P(X=4) = 0.15, and P(X\geq 7) = 0.01, we can calculate the cumulative probability P(X\leq 4) as follows:
P(X\leq 4) = P(X=1) + P(X=2) + P(X=3) + P(X=4)
= 0.25 + 0.32 + 0.18 + 0.15
= 0.9
The cumulative probability P(X\leq 4) is 0.9, which means that there is a 90% probability that there are at most 4 people in a household.
Now, to find the value of 100R, we multiply the probability P(X\leq 4) by 100:
100R = 100 * P(X\leq 4)
= 100 * 0.9
= 90
Therefore, the value of 100R is 90.