Solve the following and show your solution

1. Out of 800 families with 5 children each, how many would you expect to have either 2 or 3 boys? Assume equal probabilities for boys and girls.

2. Six cards are drawn from a deck of 52 well-shuffled cards. Find the probability that are 4 aces.

3. 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.

4. 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.

5. 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.

6. 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