📊 statistics

1. Given the data set $x = \{6, 11, 13, 17, 9, 12\}$ with mean $\mu = 11.33$. 2. To verify the population variance, we use the formula:

1. Stating the problem: Find areas under the standard normal curve for various z-values, specifically areas above or below certain z-scores or between regions. 2. Area above z = 1.

1. The problem asks us to find the area (probability) corresponding to $Z < -1.65$ on the standard normal distribution using the z-table. 2. The z-table gives the cumulative probab

1. The problem states that the mean score $\mu=32$ and the standard deviation $\sigma=5$. We are asked to find the z-score for a score $x=37$. 2. Recall the z-score formula is:

1. **State the problem:** We need to find the GPA cutoff for the highest 2.5% of students, given that GPAs are normally distributed with mean $\mu = 2.9$ and standard deviation $\s

1. **State the problem:** We are given that the volume of soda cans is normally distributed with mean $\mu=12$ oz and standard deviation $\sigma=0.25$ oz. We want to find the proba

1. The problem states that the mean life of a tire is 30,000 km and the standard deviation is 2,000 km. 2. According to the empirical rule (68-95-99.7 rule), approximately 68% of d

1. The problem asks for the range of the given data values: 2, 4, 4, 6, 7, 8. 2. The range is defined as the difference between the maximum and minimum values in the set.

1. The problem is to find the standard deviation of the data set {12, 15, 16, 12}. 2. First, find the mean (average) of the data.

1. **Problem Statement:** We are comparing anxiety levels between students receiving Cognitive Behavioural Therapy (CBT) and those receiving No Therapy. We will test if therapy red

1. **State the problem:** Given import data for 1984 from various Asian countries: $a = [297.2, 266.1, 820.1, 101.8, 431.9, 19.5, 8.4, 113.2, 3.7]$, find $a_3$, $a_4$ and compute t

1. Problem 18: Given import data from various Asian countries for years 1984 and 1985 (in million US dollars), compute the requested values a_3 and a_4. The data points (import val

1. The problem provides weekly sales data for Branch A and Branch B over five weeks. 2. To analyze, we can calculate:

1. The statement is: "Correlation Analysis has nothing to do with Regression Analysis." Let's analyze this claim. 2. Correlation analysis measures the strength and direction of a l

1. Stating the problem: We have the regression equation $$\hat{y} = b_0 + b_1 x$$ where $$b_0 = 700$$ (y-intercept) and $$b_1 = -50$$ (slope). We need to find the predicted value $

1. The regression equation is given by $$\hat{y} = b_0 + b_1 x$$ where $$b_0$$ is the y-intercept and $$b_1 = 0.5$$ is the slope. 2. The slope $$b_1 = 0.5$$ means that for every in

1. **State the problem:** We need to prepare a frequency distribution for the given data using equal class intervals of size 2.5, starting the first interval at 0.5. 2. **Identify

1. **State the problem:** We have weights of 42 students and need to

1. **Problem 1: Reading habits and conditional probabilities** Given probabilities:

1. **Problem 1: Randomized Block Design Analysis** for washing solutions effectiveness. 2. **Problem 2: Latin Square Design Analysis** for ingredients effect on reaction time.

1. **Problem statement:** We analyze a randomized block design with 3 solutions tested over 4 days to see if there is a significant difference in bacterial growth retardation at $\