📊 statistics

1. **Problem Statement:** Given the data points $(x, y)$: $$

1. **Problem Statement:** Given five observations for two variables $x$ and $y$: $x$: 4, 6, 11, 3, 16

1. **Problem:** Calculate the sample variance of the math test scores: 70, 75, 80, 85, 90. 2. **Formula:** Sample variance $s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$ wher

1. **Problem:** Calculate the sample variance of the math test scores: 70, 75, 80, 85, 90. 2. **Formula:** Sample variance $s^2 = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$ wher

1. **Problem:** Calculate the Median Deviation for the data set 5, 7, 8, 10, 15. 2. **Step 1: Find the median of the data.**

1. Let's state a basic statistics problem: Find the mean (average) of the data set: 4, 8, 6, 5, 3. 2. The formula for the mean is:

1. **Nêu bài toán:** Điều tra thu nhập của 100 công nhân được phân theo các khoảng lớp và số công nhân tương ứng. Giả sử thu nhập phân phối chuẩn, ta cần:

1. The problem asks us to create a histogram using the number of feathers Patsy sold in each of the last eight months: 19, 13, 8, 4, 7, 14, 7, 9. 2. A histogram groups data into in

1. The problem asks to create a histogram for the data points representing the points scored by the Hawaii Eagles football team: 17, 33, 28, 23, 10, 42, 3. 2. A histogram groups da

1. **State the problem:** We have a population of 15 units with values $X_i$ and $Y_i$ and random numbers $\epsilon_i$. We need to select a sample of size 7 using Simple Random Sam

1. **Stating the problem:** We have two sets of data points: $X_i$ and $Y_i$ with 15 values each. The goal is to analyze the relationship between $X_i$ and $Y_i$. 2. **Formula used

1. **Problem Statement:** Calculate the mean, variance, and standard deviation of the given probability distribution for the prizes.

1. The problem asks for the probability that a normally distributed random variable $C$ with mean $\mu=22$ and standard deviation $\sigma=8$ is less than 20, i.e., $P(C < 20)$.\n\n

1. The problem asks to identify which statement is NOT a characteristic of the normal distribution. 2. The normal distribution is a continuous probability distribution that is symm

1. **State the problem:** We want to find the probability that a randomly chosen battery lasts at least 135 hours, given the battery life is normally distributed with mean $\mu = 1

1. **Problem statement:** We want to find the probability that a randomly chosen battery lasts at least 135 hours, given that the battery life is normally distributed with mean $\m

1. **State the problem:** We have a population with mean $\mu = 80$ and standard deviation $\sigma = 5$. We draw random samples of size $n = 100$. We want to find the mean of the s

1. **State the problem:** We want to select the correct statistical hypotheses to test the mean arsenic level $\mu$ in residential drinking water and then find a 95% confidence int

1. The problem asks for the regression equation of a quadratic model based on the given data points relating Instagram screen time and number of alcohol-impaired driving deaths. 2.

1. **Problem Statement:** We have a normal distribution with mean $m = 23.6$ kg and standard deviation $\sigma = 1.8$ kg.

1. The problem asks to find the percentage of data between the z-scores $-0.14$ and $0.09$ in a standard normal distribution. 2. We use the standard normal distribution table (Z-ta