 ### Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of X+Y.

Mean Standard Deviation $X$ $80$ $12$ $Y$ $12$ $3$ The purpose of this question is to find the mean and standard deviation of the given expression using the expected values and standard deviations of the random variables given in the table. A random variable numerically represents the result of a trial. Two types of […]

### How many ways are there to distribute six indistinguishable balls into nine distinguishable bins?

The objective of this question is to find the number of ways the six indistinguishable balls can be distributed into nine distinguishable bins. A mathematical method for determining the number of potential groupings in a set of objects in which the selection order becomes irrelevant is referred to as combination. The objects can be chosen […]

### The seller of a loaded die claims that it will favor the outcome 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain.

There’s a $3%$ chance that the die is fair. There’s a $97%$ chance that the die is fair. There’s a $3%$ chance that a loaded die could randomly produce the results we observed, so it’s reasonable to conclude that the die is fair. There’s a $3%$ chance that a fair die could randomly produce the […]

### A pair of honest dice is rolled once. Find the expected value of the sum of the two numbers rolled.

This question aims to find the expected value of the sum of two numbers in rolling a pair of dice. A common example of a random trial is when a die is rolled. It is an act in which we can itemize all the attainable results that can be listed but the exact result on […]

### Which of the following is NOT a conclusion of the Central Limit​ Theorem? Choose the correct answer below.

The distribution of the sample means $x$ over $bar{x}$ will, as the sample size increases, approach a normal distribution. The distribution of the sample data will approach a normal distribution as the sample size increases. The standard deviation of all sample means is the population standard deviation divided by the square root of the sample […]