📊 statistics

1. The problem asks to find the area under the standard normal curve for various ranges of the variable $z$. 2. The standard normal distribution is a normal distribution with mean

1. **State the problem:** We want to test if the mean anxiety level of a sample of 30 individuals differs from the population norm of 50. 2. **Set hypotheses:**

1. **Problem statement:** We have a frequency distribution of blood glucose levels for 100 diabetics with intervals and frequencies given. We need to construct the histogram and cu

1. **State the problem:** We are given the regression line equation $$y = -\frac{2}{3}x + \frac{125}{3}$$ which estimates IB Diploma points ($y$) based on hours spent on social med

1. State the problem: Complete the probability table and compute the mean $\mu$, the variance $\sigma^2$, and the standard deviation $\sigma$ for the given discrete distribution. 2

1. **Stating the problem:** We have measured 10 mechanical parts and recorded their deviations (gaps) from a fixed length. The gaps and their frequencies are: | Gap (mm) | 0 | 1 |

1. **State the problem:** We are given the regression line equation for IB Diploma points $y$ based on hours spent on social media $x$ for 10 female students:

1. **Stating the problem:** We are given a box and whisker diagram representing the number of sick days taken by employees in a year. We need to identify the minimum, lower quartil

1. **Problem Statement:** Use the least squares method to develop a linear trend equation for the annual aluminum shipments data from 1989 to 1999 and forecast the shipment for the

1. **State the problem:** We are given the regression line equation for IB Diploma points $y$ based on hours spent on social media $x$ for ten female students:

1. **State the problem:** We have data for 8 male students showing hours spent on social media ($x$) and their IB Diploma points ($y$). We need to plot a scatter diagram, calculate

1. **Problem Statement:** We have a box and whisker diagram representing the number of sick days taken by employees in a year. The key values are:

1. **Problem 5a:** Show that the test score of 25 is not an outlier given the lower quartile (Q1) = 62 and upper quartile (Q3) = 88. 2. **Formula and rule:** To check for outliers,

1. **Problem statement:** We have water temperature data $T$ for months $m=1$ to $8$ (January to August) with May ($m=5$) missing. We assume a linear model $T=am+b$ and want to fin

1. **Problem statement:** We have a sample of 760 potatoes with weights measured and a cumulative frequency curve given. We need to find: - (a) Number of potatoes weighing more tha

1. **Problem statement:** A school has 740 students divided into 5 grades with given numbers. The principal wants to select a sample of 25 students maintaining the same proportion

1. **Stating the problem:** We are given a list of squared deviations from the mean, $(x - \bar{x})^2$, and we need to find their sum, which is the numerator in the standard deviat

1. The problem is to find the Interquartile Range (IQR) of a data set. 2. The IQR is a measure of statistical dispersion and is calculated as the difference between the third quart

1. The problem is to find the first quartile (Q1), median (Q2), and third quartile (Q3) of the given data set. 2. First, sort the data in ascending order:

1. **Problem Statement:** Determine if there is a significant change in resiliency levels before and after undergoing Gestalt Therapy using the given data. 2. **Step 1: Calculate M

1. **State the problem:** We need to find the first four central moments and the first three moments about the origin 4 for the data set $\{2,4,6,8\}$. 2. **Recall definitions:**