Solve the following problem/s and Show your solution

1. A factory finds that, on average, 10% of the bulb produced by a given machine will be defective for certain specified requirements. If 8 bulbs are selected at random from the day's production of this machine, find the probability that more than 5 will be defective.
2. . A box contains 5 green, 3 red, and 2 black balls. If 3 balls are drawn at random, determine the probability that at least 1 is red.
3. If X is normally distributed with a mean of 5 and standard deviation of 2, find the P(X>8).
4. A sample of 150 students was considered with a mean weight of 65 kilos and the standard deviation of 5 kilos. Find how many students weigh between 60 and 70 kilos.
5. On an examination, the average grade was 76 and the standard deviation was 6. If 9% of the class are given 1.5 and the grades are as to follow, compute the lowest and highest possible grade for 1.5.
6. The number of accidents occurring at a certain intersection with a mean of 3 accidents every 5 days. What is the probability that exactly 2 accidents will occur in the next 5 days.