Please kindly solve these problems with explanation.

q1. A sample size of 8 items has an average fat content of 18.6 grams and a standard deviation of 2.4 grams. Assuming a normal distribution, construct a 99 percent confidence interval for

q2. In a survey of 1000 people, 420 are opposed to the tax increase. Construct a 95 percent confidence interval for the proportion of those people opposed to the tax increase.

q3. The diameter of small nerf balls manufactured at a factory in china is expected to be approximately normally distributed with a mean of 5.2 inches and a standard deviation of 0.08 inches. Suppose a random sample of 20 balls are selected. What percentage of sample mean will be less than 5.15 inches?

q4. Test at = 0.05, the hypotheses H0: 0.33 versus H1: < 0.33 with p = 0.23 and n=100

q5. The JO supplies company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 14 calculators are selected at random, what is the probability that less than 5 of the calculators will be defective?

q6. If x is a binomial random variable where n=100 and p=0.30, find the probability that x is greater than or equal to 35 using the normal approximation to the binomial. (discuss whether continuity correction is necessary or not)

q7. Given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet, what is the probability he throws it between 42 feet and 62 feet?