📊 statistics

1. **Problem Statement:** We are given that 40% of all murders are domestic homicides, and a study selects 10 murder cases. We want to find the probability that between 1 and 3 of

1. **Stating the problem:** We are given two regression lines:

1. **State the problem:** We want to find the regression lines given the mean of $x$ ($\bar{x}$), mean of $y$ ($\bar{y}$), correlation coefficient $r$, and standard deviations $s_x

1. Problem 4: Given \(\sum x = 90\), \(\sum x^2 = 308\), \(\sum y^2 = 27218\), \(\sum xy = 1617\), \(\sum y = 1010\), find the regression line of \(y\) on \(x\). Formula for regres

1. **Problem statement:** We have a cumulative frequency table for the diameters of 60 oranges and need to (a) draw the cumulative frequency graph and (b) estimate the median diame

1. **State the problem:** We are given a data set of 13 distances to the nearest airport: 9, 10, 12, 12, 20, 21, 22, 23, 26, 32, 35, 35, 37. We need to find the median, lower quart

1. **State the problem:** Diane's home price is $737000. The mean home price in the area is $785000 with a standard deviation of $18050. We need to find the z-score of Diane's home

1. **State the problem:** We need to find the standard deviation of the sample salaries: 13, 10, 9, 11, 7 (in thousands). 2. **Formula for sample standard deviation:**

1. **State the problem:** We are given the ages of 6 employees: 26, 38, 26, 29, 28, 39. We need to find the population standard deviation of these ages, rounded to two decimal plac

1. **Problem Statement:** We have reaction times (in milliseconds) from 8 trials: 444, 444, 567, 309, 345, 309, 524, 741. We need to find:

1. **Problem Statement:** Calculate the regression coefficients of $Y$ on $X$ and find the regression equation for the given data: | X | 1 | 3 | 4 | 6 | 8 | 9 | 11 | 14 |

1. The problem asks for the meaning of a "tie" in rank analysis in correlation. 2. In rank correlation methods like Spearman's rank correlation coefficient, data values are convert

1. **Problem Statement:** We have three variables: $X_1$ (Average diameter), $X_2$ (Height), and $X_3$ (Volume) for 9 trees. We need to find correlations and test hypotheses involv

1. **State the problem:** We are given a mean $\mu = 77$ and a standard deviation $\sigma = 14$. We need to find the z-score values for given scores. 2. **Formula for z-score:** Th

1. The problem is to understand how the p-value is found on the GDC (Genomic Data Commons) platform. 2. The p-value is a statistical measure that helps determine the significance o

1. **State the problem:** We want to test if the new typing exercise method has a better success rate than the traditional method. The probability of success is $p$. 2. **Set hypot

1. **State the problem:** We want to test if the new exercises have a higher success rate than the traditional method, which has a success rate of 70% (or 0.7). 2. **Set up hypothe

1. **State the problem:** We want to test if the fuel economy of E10 fuel is the same as regular unleaded fuel using a paired t-test at a 5% significance level. 2. **Data given:**

1. সমস্যাটি হলো: জীববিজ্ঞান ও পরিসংখ্যান বিষয়ের নম্বর থেকে সংশ্লেষাংক (correlation coefficient) নির্ণয় করা। 2. সংশ্লেষাংক নির্ণয়ের সূত্র হলো: $$r = \frac{n\sum xy - \sum x \sum y}{

1. The problem involves understanding proportions in a population to plan a survey for launching new dishes. 2. We know 75% of customers are female and 25% are male.

1. **Stating the problem:** We have a two-way table showing the number of men and women workers who either have a problem or no problem with wage levels for men and women doing the