Question

A certain insecticide kills 60% of all insects in laboratory experiments. A sample of 12 insects is exposed to the insecticide in a particular experiment. What is the probability that no more than 9 insects will die? Round your answer to four decimal places.

a) 0.0884
b) 0.9116
c) 0.3200
d) 0.6800

Answer 1

To find the probability that no more than 9 insects will die, you need to calculate the probability of each possible outcome and add them up. The probability that no more than 9 insects will die is 0.0884.

Step-by-step explanation:

To find the probability that no more than 9 insects will die, we need to calculate the probability of each possible outcome and add them up.

1. The probability of 0 insects dying is calculated as: (0.4)^12 = 0.0000061.
2. The probability of 1 insect dying is calculated as: 12C1 x (0.4)^1 x (0.6)^11 = 0.0000915.
3. Similarly, calculate the probabilities for 2, 3, 4, 5, 6, 7, 8, and 9 insects dying using the same formula.
4. Add up all the calculated probabilities.

The probability that no more than 9 insects will die is the sum of all the calculated probabilities, rounded to four decimal places: 0.0884.