📊 statistics

1. **Problem Statement:** We have a sample of 15 waiting times in minutes: 1.38, 2.34, 3.02, 3.20, 3.54, 3.79, 4.21, 4.50, 4.77, 5, 5.13, 5.35, 5.55, 6.10, 6.19. We need to constru

1. **Problem:** Find the area under the standard normal curve for z between 1.03 and 2.79. 2. **Formula:** The area between two z-values $z_1$ and $z_2$ is given by $P(z_1 < Z < z_

1. **Problem Statement:** Calculate the variance of profit data given in class intervals with frequencies. 2. **Understanding the Data:** We have profit intervals (0-10, 10-20, etc

1. **Problem statement:** Given a binomial distribution with mean $\mu = 4$ and variance $\sigma^2 = \frac{4}{3}$, find the probability $P(X > 1)$. 2. **Recall formulas for binomia

1. **Problem Statement:** Calculate the median of grouped data using the formula and understand its components. 2. **Formula for Median of Grouped Data:**

1. Muammo: Berilgan statistik ma'lumotlar asosida tanlanma o'rtacha qiymat $X_T$, dispersiya $D_T$ va standart og'ish $C3$ ni hisoblash. 2. Formulalar va qoidalar:

1. **Problem Statement:** We want to find the mean weekly earning of employees using the step-deviation method from the given grouped data. 2. **Understanding the Table:** The tabl

1. **Problem Statement:** We want to determine if 7 hours of sleep deprivation significantly increases reaction time using the given before and after data for 10 subjects. 2. **Tes

1. **Problem Statement:** We want to test if the weight-reducing plan is effective. We have weights before and after the plan for 11 people. We will use a paired t-test at a 0.05 s

1. **Problem Statement:** We have monthly data of the number of software file updates for 12 months. We need to create a variable control chart by finding the center line, upper co

1. **Stating the problem:** You asked where each number in the quartile calculation example comes from. 2. **Data set:** The numbers come from the sorted data set $[2, 4, 7, 10, 12

1. **Stating the problem:** We want to find which quartile a given number belongs to in a data set. 2. **Understanding quartiles:** Quartiles divide data into four equal parts. The

1. Állítsuk fel a problémát: A konzerv töltőtömege normális eloszlású, várható értéke $\mu=100$ g, és a töltőtömegek 16%-a kisebb, mint 99,1 g. Meg kell határoznunk a szórást $\sig

1. Állítsuk fel a feladatot: A konzerv töltőtömege normális eloszlású, várható értéke $\mu=100$ g. 2. Tudjuk, hogy a töltőtömeg 16%-a kisebb, mint 99,1 g, azaz

1. **הבעיה:** נתונה טבלה המתארת את הקשר בין מרחק מנוי ירוק (בק"מ) לבין משכורת (בדולרים) של מהנדס חשמל.

1. **State the problem:** Find the interquartile range (IQR) from the given frequency distribution with intervals and frequencies: | Interval | Frequency (f) |

1. **הבעיה:** יש לנו נתונים של שעות שינה (y) וגיל (x) עם סטטיסטיקות נתונות: $S_y=1.724$, $S_x=5.85$, $r=-0.99424$, $5=10.6$, $5=10.5$. עלינו לקבוע איזה מהגרפים (I או II) מציג את

1. The problem involves calculating the z-score using the formula $$z = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$$ where $\bar{X}$ is the sample mean, $\mu$ is the population

1. **Problem Statement:** Test if there has been an increase in the proportion of drivers who text while driving from last year (17%) to this year (29%) using a 99% confidence inte

1. **Problem:** Calculate the mean and median of the corn production data (in millions of bushels) for seven states: 27, 692, 700, 342, 191, 148, 311. 2. **Formula and rules:**

1. **State the problem:** We are given two variables, $Y$ (Sales) and $x$ (Adv), and we want to find the estimated linear regression equation of the form $$Y = b^0 + b^1 x$$ where