 ### Two stores sell watermelons. At the first store, the melons weigh an average of 22 pounds, with a standard deviation of 2.5 pounds. At the second store, the melons are smaller, with a mean of 18 pounds and a standard deviation of 2 pounds. You select a melon at random at each store.

Find the mean difference in weights of the melons? Find the standard deviation of the difference in weights? If a Normal model can be used to describe the difference in weights, find the probability that the melon you got at the first store is heavier? This question aims to find the mean difference and standard […]

### Let X be a normal random variable with mean 12 and variance 4. Find the value of c such that P(X>c)=0.10.

This question aims to find the value of $c$ given the probability distribution of a random variable $X$. In probability theory, a random variable is regarded as a real-valued function that is defined over a sample space of a random experiment. In other words, it describes the outcome of an experiment numerically. Random variables can […]

### Which of the following are possible examples of sampling distributions? (Select all that apply.)

the mean trout lengths based on samples of size $5$. the average SAT score of a sample of high school students. the average male height based on samples of size $30$. the heights of college students at a sampled university all mean trout lengths in a sampled lake. In this question, we need to choose […]

### Let x represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible values of X?

The aim of this question is to understand the key concept of a random variable using the coin toss experiment which is the most basic binomial (experiment with two possible outcomes) experiment performed in probability theory. A random variable is nothing but a mathematical formula used to describe the outcome of statistical experiments. For example, […]