Suppose x has a normal distribution with a population standard deviation of 2.2. If a random sample of size 31 had a sample mean of 66, find a 98% confidence interval for µ.

An SRS of size 10 is drawn from a population that has a normal distribution. The sample has a mean of 139 and a standard deviation of 7. Give the standard error of the mean 7 , 1

A company that makes cola drinks states that the mean caffeine content per​ 12-ounce bottle of cola is 35 milligrams. You want to test this claim. During your​ tests, you find that a random sample of thirty​ 12-ounce bottles of cola has a mean caffeine content of 35.4 milligrams. Assume the population is normally distributed and the population standard deviation is 7.9 milligrams. At α=0.05​, can you reject the​ company's claim? Complete parts​ (a) through​ (e).   Part 1​(a) Identify H0 and Ha.   Choose the correct answer below. A.) H0​:μ≥35.4       Ha​:μ<35.4   B.) H0​:μ≠35       Ha​:μ=35   C.) H0​:μ=35       Ha​:μ≠35   D.) H0​: μ≥35       Ha​: μ<35   E.) H0​: μ≠35.4      Ha​:μ=35.4   F.) H0​: μ=35.4     Ha​:μ≠ 35.4   (b) Find the critical​ value(s). Select the correct choice below and fill in the answer box within your choice.   ​(c) Find the standardized test statistic.       z=   ​(d) Decide whether to reject or fail to reject…

Assume the random variable X is normally distributed with mean μ=50 and standard deviation σ=7. Find the 87th percentile.