Please help with these homework questions and explain the procedure. Will rate immediately thank you very much.

1.- A fabric manufacturer believes that the proportion of orders for raw material arriving late is p = 0.6. If a random sample of 10 orders shows that 3 or fewer arrived late, the hypothesis that p = 0.6 should be rejected in favor of the alternative p < 0.6. Use the binomial distribution.

(a) Find the probability of committing a type I error if the true proportion is p = 0.6.

(b) Find the probability of committing a type II error for the alternatives p = 0.3 and p = 0.5.

2.- A random sample of 100 automobile owners in a state shows that an automobile is driven on average 23,500 kilometers per year. It is known that the population standard deviation is 3,900 kilometers. Assume the distribution of measurements to be approximately normal.

(a) Construct a 95% confidence interval for the average number of kilometers an automobile is driven annually in this state.

(b) Do the same as in part (a) but with a 99% confidence interval.

3.- A random sample of 64 bags of white cheddar popcorn weighed, on average, 5.23 ounces with a standard deviation of 0.24 ounce. Test the hypothesis that = 5.5 ounces against the alternative hypothesis, < 5.5 ounces, at the 0.05 level of significance.