📊 statistics

1. Let's start by defining the problem: finding the mean (average) of a set of values given in a table. 2. The mean is calculated by summing all the values and then dividing by the

1. **State the problem:** Andy believes 83% of his customers are satisfied with the food. A random sample of 99 customers is taken. We want to find probabilities related to the num

1. **Problem Statement:** Calculate acceptance probability for a lot with $N=25$ items, 2 nonconforming, selecting a sample of 5 without replacement. 2. **Exact hypergeometric prob

1. **Question 1: Acceptance probability for lot size $N=25$ with 2 nonconforming** (a) Problem: Probability of lot acceptance means selecting 0 nonconforming components in a sample

1. **Acceptance Probability, Lot Size N=25, 2 Nonconforming** (a) Probability all 5 selected are conforming (Hypergeometric):

1. **Problem:** Calculate acceptance probability with lot size $N=25$ and 2 nonconforming. (a) Calculate hypergeometric probability $P=\frac{\binom{23}{5}}{\binom{25}{5}}$ with $23

1. **Question 1**: Acceptance probability when lot size $N=25$ and 2 nonconforming components. (a) The probability of lot acceptance means no nonconforming components are selected

1. The problem asks for the number of values in the interval from 0 to 2, as well as the interval with the most values. 2. From the histogram data given, the number of values in ea

1. The problem asks for the number of students who have a number of coins in the range $$6 \leq \text{number of coins} < 9$$. 2. According to the histogram description, the bar ove

1. The problem asks to find the median of the data given in class intervals with frequencies. 2. The class intervals are: 5-9, 10-14, 15-19, 20-24, 25-29, 30-34, but the frequency

1. The problem is to find the median of the given data. However, the frequencies corresponding to each class interval are missing, which are essential for calculating the median. 2

1. **Problem 10: Scatter Diagram and Correlation Sign** Given data:

1. Problem 10: Draw a scatter diagram for Mathematics and Statistics marks and determine correlation. - Mathematics marks: $15, 18, 21, 24, 27, 30, 36, 39, 42, 48$

1. **Problem Statement:** Calculate the mean, median, and mode of students' scores given the frequency distribution. 2. **Given Data:**

1. The problem is to find the values of \(\beta_0, \beta_1, \beta_2\) that minimize the sum of squared differences given by $$\sum_{i=1}^{30} \left( \text{Milk Yield}_i - \beta_0 -

1. **Problem:** Fit a multiple regression model predicting milk yield using cow body weight and age as predictors. 2. **Step 1: Define the regression model.**

1. **State the problem:** Calculate the correlation coefficient $r$ between heights and weights of 50 individuals based on the given frequency table. 2. **List values:** Heights $X

1. **Calculate the range of the data recorded.** The data marks of 21 learners are: 15, 7, 11, 7, 13, 4, 8, 9, 3, 7, 25, 7, 6, 10, 8, 9, 23, 19, 7, 5, 7.

1. **Calculate the range of the data recorded.** The range is the difference between the highest and lowest marks.

1. **Problem Statement:** Calculate the Pearson correlation coefficient between the dependent variable $Y$ (monthly labor hours) and each independent variable $X1, X2, X3, X4,$ and

1. **Problem 3: Analyze the 4x4 Latin Square Design for assembly methods and operators (α = 0.05).** Given a Latin square for assembly method (A, B, C, D) by 4 operators with time