Question

60% of those who use the internet do their homework online. If 8 kids are randomly selected, what is the probability that no more than 5 will do their homework online?

a) 0.16384
b) 0.32768
c) 0.4096
d) 0.5904

Answer 1

The probability that no more than 5 out of 8 kids will do their homework online is d) 0.5904.

Step-by-step explanation:

To find the probability that no more than 5 out of 8 kids will do their homework online, we can use the binomial probability formula.

Let X represent the number of kids doing their homework online.

Then we have n=8 (number of trials) and p=0.60 (probability of success).

Now, we need to calculate the probability of X ≤ 5. We can do this by calculating the individual probabilities of X = 0, 1, 2, 3, 4, and 5, and then adding them up.

P(X = 0) = (8 choose 0) * (0.60)^0 * (1-0.60)^(8-0)

P(X = 1) = (8 choose 1) * (0.60)^1 * (1-0.60)^(8-1)

P(X = 2) = (8 choose 2) * (0.60)^2 * (1-0.60)^(8-2)

P(X = 3) = (8 choose 3) * (0.60)^3 * (1-0.60)^(8-3)

P(X = 4) = (8 choose 4) * (0.60)^4 * (1-0.60)^(8-4)

P(X = 5) = (8 choose 5) * (0.60)^5 * (1-0.60)^(8-5)

Finally, we sum up all these probabilities:

P(X ≤ 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

After calculating the probabilities, we find that the answer is 0.5904.