📊 statistics

1. Problem 1: Find the probability that the sample mean score is less than 70 given $X \sim N(65, 23^2)$ and sample size $n=45$. 2. Use the Central Limit Theorem: The sampling dist

1. **State the problem:** Find the 10th, 25th, 50th, 75th, and 95th percentiles of the data set: 40, 45, 50, 56, 60, 65, 65, 80, 90. 2. **Sort the data:** The data is already sorte

1. **Problem Statement:** (a)(i) Find the mean of the monthly allowances of 7 students: 1200, 1100, 800, 600, 550, 900, 750.

1. **State the problem:** Calculate the mean (average) of the given data set A: 102, 105, 122, 125, 127, 129, 130, 144, 155. 2. **Formula for mean:** The mean of a data set is give

1. **Problem Statement:** Calculate the mean of each data set (Data A, B, C, D, E) and round the answers to two decimal places. 2. **Formula for Mean:**

1. **Problem Statement:** Calculate the probability that between 4 or 5 beta testers out of 18 successfully adopt a new software feature within the first week, given the success pr

1. **Stating the problem:** We want to test if the given frequency distribution data follows a normal distribution using the Chi-Square goodness-of-fit test at significance level $

1. **Stating the problem:** We want to understand what the sample correlation coefficient $r$ measures and determine which value indicates a stronger correlation between $r=0.918$

1. Problem 1: Hypothesis test for population proportion. We want to test if the population proportion $p$ of households loyal to brand W is greater than 0.48.

1. **State the problem:** We want to test if the population proportion of households loyal to brand W cloth washing liquid is greater than 48% based on a sample of 100 households w

1. **Problem statement:** The weekly sales amount of a skin care product follows a normal distribution with mean $\mu=5000$ and standard deviation $\sigma=400$. We need to find pro

1. **Stating the problem:** We want to analyze the influence of motivation at work ($X_1$) and work spirit ($X_2$) on employee performance ($Y$) using multiple linear regression.

1. **Problem Statement:** Compute all the remaining possible class frequencies from the given data: $\alpha = 50$, $\beta = 70$, $(AB) = 20$, and total $n = 100$.

1. समस्या को समझें: हमें 15 अभ्यर्थियों के अंक दिए गए हैं जिनमें से कुछ ने परीक्षा उत्तीर्ण की है। उत्तीर्ण अभ्यर्थियों के अंक हैं: 9, 6, 7, 8, 8, 8, 9, 6, 5, 4, 7। हमें इन अंक की

1. **State the problem:** Find the area under the normal distribution curve between $70 < X < 95$ where the mean $\overline{x} = 100$ and standard deviation $\sigma = 10$. 2. **For

1. **State the problem:** Find the area under the normal distribution curve between $70 < X < 95$ where the mean $\overline{x} = 100$ and standard deviation $\sigma = 10$. 2. **For

1. **Stating the problem:** We are given a frequency distribution and asked to calculate the mean using the relationship among mode, median, and mean. 2. **Understanding the relati

1. **Stating the problem:** We are given a distribution and asked to calculate the mean using the relationship among mode, median, and mean. 2. **Recall the formula:** For moderate

1. **Stating the problem:** We have a dataset of absences over 18 days: 4, 3, 0, 1, 2, 5, 6, 8, 10, 7, 11, 15, 19, 13, 4, 2, 12. 2. **Goal:** To create a frequency distribution wit

1. **Problem Statement:** We have marks of 25 students in a class test out of 5: 40, 0.8, 4.5, 1.3, 3.5, 5, 2.5, 4.0, 2.5, 1.6, 2.0, 4.6, 3.0, 8.5, 0.9, 1.0, 2.0, 2.0, 4.5, 2.5, 3.

1. **Problem Statement:** Given the distribution data: 1 3 2 1 4 2 5 8 5 6 478 5 7 15 8 3556788999 26 9 12344568889 45 10 0123444445567888899 17 11 00122235555556889 38 12 01112222