📊 statistics

1. **State the problem:** We have a metal component's tensile strength $X$ that is normally distributed with mean $\mu = 10000$ and standard deviation $\sigma = 100$. We want to fi

1. **State the problem:** Calculate Karl Pearson's Coefficient of Skewness for the given frequency distribution. 2. **Given data:**

1. **Problem 1: Find the Pearson correlation coefficient $r$ between Physics and Chemistry scores and test its significance at the 0.05 level.** 2. Calculate the means:

1. **State the problem:** We have 31 test scores out of 100 and want to standardize them using the formula $$z_i = \frac{x_i - \text{mean}}{SD}$$ and then convert to a scale with m

1. The problem is to standardize the given test scores out of 100 and find the exact total marks after standardization. 2. First, list the scores: 16, 0, 28, 12, 0, 78, 46, 0, 4, 1

1. **State the problem:** We have a set of test scores out of 100, and we want to standardize these marks to better understand their distribution. 2. **List the scores:** 16, 0, 28

1. **State the problem:** Sarah wants to select a sample of 30 people from 210 people using systematic sampling. We need to find the skip interval $k$, the probability that a parti

1. **Problem 1: Sample size using Slovin's formula with 2% margin of error** Slovin's formula for sample size $n$ is:

1. **State the problem:** We are given class intervals and their corresponding frequencies, and we need to calculate the standard deviation of the data. 2. **List the class interva

1. **State the problem:** We are given sales data grouped into intervals with the number of sales staff in each interval. We need to present this data as an Ogive, which is a cumul

1. **State the problem:** We have data points for price $x$ and profit $y$: | Price ($x$) | Profit ($y$) |

1. The problem asks us to estimate the number of medium oranges in the box, where medium oranges weigh between 35 grams and 55 grams. 2. From the histogram data, the frequency dens

1. The problem asks if it would be surprising for Djokovic to hit a first serve between 120 and 130 mph. 2. From the answer bank, the relevant probabilities are:

1. **State the problem:** We want to find the proportion of Djokovic's first serves with speeds between 120 mph and 130 mph, given that the speeds are normally distributed with mea

1. **State the problem:** We want to find the probability that Novak Djokovic's first serve speed is at least 110 mph, given that the serve speed follows a normal distribution with

1. **State the problem:** We want to test if the treatment (Drug or Placebo) is independent of the side effect of nausea at significance level $\alpha=0.10$ using the given conting

1. **Problem 1: Construct a 95% confidence interval for the population mean life of light bulbs.** Given:

1. **Problem 1:** Construct a 95% confidence interval estimate of the population mean life for light bulbs. 2. Given:

1. **State the problem:** We need to calculate the range and standard deviation of monthly rainfall for City A and City B over 6 months, then determine which city has more variabil

1. **Problem Statement:** Given data for hours spent studying (X) and exam scores (Y), we need to find: a. Sample linear correlation coefficient $r$

1. **State the problem:** We have 10 articles with comment counts: $\{15, 25, 10, 30, 20, 18, 22, 12, 28, 17\}$. We need to calculate the mean and standard deviation of these comme