📊 statistics

1. **Problem Statement:** We have fly ball distances normally distributed with mean $\mu=234$ feet and standard deviation $\sigma=56$ feet. We sample $n=49$ fly balls and want to f

1. **Problem Statement:** We have 49 fly balls with an average distance traveled, and we want to find the probability that the average distance is less than 222 feet.

1. The problem asks for the probability that the average distance traveled by 49 balls is less than 222 feet. 2. We use the Central Limit Theorem which states that the sampling dis

1. **Problem 1:** Find the time $t$ such that 80% of the time, it takes more than $t$ minutes to find a parking space. Given: $X \sim N(6, 2^2)$ (mean $\mu=6$, standard deviation $

1. **Problem Statement:** We are given the areas of sprayable surfaces from 15 houses and need to find the variance and standard deviation of this data set. 2. **Data:** 101, 105,

1. **State the problem:** We want to analyze if there is a significant difference in depression levels among three therapy groups using ANOVA. The null hypothesis $H_0$ states no d

1. **State the problem:** We want to analyze if different types of therapy have different effects on depression scores using ANOVA. 2. **Given data:**

1. The problem is to select a simple random sample without replacement using a table of random numbers for three different cases. 2. Simple random sampling without replacement mean

1. The problem involves understanding different sampling methods and their applications in statistics. 2. For (iii), examining a shipment of electric bulbs to obtain information on

1. **Problem Statement:** Find the 10th percentile of the given data set. 2. **Understanding Percentiles:** The $p$th percentile is the value below which $p\%$ of the data falls. T

1. **State the problem:** Find the median of grouped data given the class intervals and their frequencies. 2. **Given data:**

1. The problem is to understand basic statistics concepts typically covered in class 10, such as mean, median, mode, and range. 2. The mean (average) of a data set is calculated us

1. **Problem Statement:** We are given descriptive statistics for Higher Order Thinking (HOT) scores by mode of delivery and class size. We need to perform ANOVA and t-tests to ana

1. **Problem Statement:** A farmer collected data on fertilizer amount $x$ (hundreds of kgs per acre) and soya bean yield $y$ (bushels per acre). We analyze the relationship betwee

1. **Problem Statement:** We want to build a linear regression model to predict house prices based on size (sq ft) and age (years) using the given data.

1. **Stating the problem:** We have two sequences of data: one representing batch deliveries and another representing evaluation marks for Charlie's activities. 2. **Understanding

1. **Problem Statement:** We have a frequency distribution of scores in intervals and their corresponding frequencies. We want to understand the data and possibly find measures lik

1. **State the problem:** We have a frequency distribution with class intervals and frequencies: 0-20 (6), 20-40 (8), 40-60 ($f_1$), 60-80 (12), 80-100 (6), 100-120 (5). The mode i

1. **State the problem:** We have Mikaeel's reading times over 7 days: 35, 30, 39, 35, 35, 22, 42 minutes. We need to find the mean, median, mode, range, check for outliers, and ex

1. **Problem:** Determine if there is a significant difference in average sales between salesmen A and B using a t-test at 5% significance level. 2. **Given:**

1. **Stating the problem:** We are given a grouped frequency distribution table with class intervals, frequencies, class marks, and other statistical values. We want to understand