This involves questions about finding probabilities and X values that involve the normal distribution and the sampling distribution of the mean and proportion

All answer should be rounded to 2 decimal places.

A can of paint contains a mean of 5 litres of paint with a standard deviation of 0.2 litres. The amount of paint is normally distributed.

1. What is the probability that a can of paint has less than 4.9 litres?
2. What percent of cans of paint have more than 5.1 litres?
3. What proportion of cans of paint (between 0 and 1) have between 4.9 and 5.1 litres?
4. What is the 85^th percentile of quantity of paint in a can?
5. 95% of cans of paint have between ______ and ______ (the middle 95%, so that these values are symmetrically distributed around the mean.

A delivery truck carries 100 cans of paint (a random sample of 100 cans the same cans as in part one with a mean volume of 5 litres of paint with a standard deviation of 0.2 litres).

6. What is the mean of the sampling distribution of the sample mean (X)?
7. What is the standard error of the sampling distribution of the sample mean?
8. What is the probability that, on average, the amount of paint per can in the truck is less than 4.9 litres?
9. The standard deviation, when we were looking at only a single can of paint, was ______ times the SE in this question.
10. Because the SE is smaller now, the X value is less likely/more likely to be close to .

A police informant says that 10% of the delivery trucks are used to smuggle illegal drugs. There will be 100 delivery trucks this month.

11. What is the mean of the sampling distribution of the proportion (p)?
12. What is the standard error of the sampling distribution of the proportion?
13. What is the probability that over 15% of the trucks are used to smuggle illegal drugs?
14. If you look at 10000 trucks instead of 100 trucks the SE will be smaller/larger?
15. Continuing the question of 14, by what factor?