📊 statistics

1. The problem asks for the area under the standard normal curve to the left of $z=1.42$. This area represents the cumulative probability $P(Z \leq 1.42)$ where $Z$ is a standard n

1. The problem asks for the probability that a standard normal variable $Z$ lies between $-2.85$ and $1.74$, i.e., $P(-2.85 < Z < 1.74)$. 2. For a standard normal distribution, pro

1. The problem asks to find the value of $k$ such that the area to the right of $k$ under the standard normal distribution curve is $P(z>k) = 0.9991$. 2. This means we want to find

1. The problem asks for the area under the standard normal curve to the right of $z = -2.34$. 2. The standard normal distribution is symmetric about zero, and the total area under

1. **State the problem:** We have a sample data set: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55. We want to find the new standard deviation if every observation is multiplied by 3.

1. **State the problem:** We need to find the variance of the ages of 16 employees given the data: 22, 58, 25, 35, 35, 40, 40, 35, 43, 53, 47, 22, 53, 35, 58, 25. 2. **Formula for

1. The problem is to find the formula for the median in grouped data. 2. The median is the value that divides the data into two equal halves.

1. The problem is to find the formula for the median of grouped data. 2. The median is the value that divides the data into two equal halves.

1. **State the problem:** We are given a standard normal distribution with a shaded area representing the probability 0.2881 between 0 and $h$. We need to find:

1. **State the problem:** We have a normal distribution for replacement times with mean $\mu = 12.6$ years and standard deviation $\sigma = 1.5$ years.

1. Mann-Whitney U Test: - Purpose: To compare differences between two independent samples when data is not normally distributed.

1. **Mann-Whitney U Test** - This test compares differences between two independent groups when the dependent variable is either ordinal or continuous but not normally distributed.

1. **Problem Statement:** Construct a frequency distribution table (FDT) for the given student scores using a class interval of 6, starting with the lowest value as the lowest lowe

1. **Stating the problem:** We want to derive the underlying relation between Correspondence Analysis (CA) and Chi-Square ($\chi^2$) analysis of association. 2. **Background:**

1. Let's first understand what the standard error is. The standard error measures the variability or precision of a sample mean estimate of a population mean. 2. You need to calcul

1. **State the problem:** We want to construct a 90% confidence interval for the mean age at which toddlers first put two words together based on a sample of 6 toddlers with ages:

1. The problem asks to identify the important feature omitted in a poll summary that includes a sample size, a point estimate, and a margin of error. 2. Given data:

1. مسئله: نمودار جعبه‌ای (Box plot) را با توجه به داده‌های داده شده بسازیم. داده‌ها: $\text{min} = 3$, $Q_1 = 7$, $\text{median} = 10$, $Q_3 = 19$, $\text{max} = 24$ (چون $R = 21 -

1. **State the problem:** We want to test if the standard deviation $\sigma$ of the golf professional's scores on his home course is equal to 1.20 (null hypothesis) against the alt

1. **State the problem:** We are given grouped data for the thickness of books and their frequencies. We need to estimate the mean thickness. 2. **Formula for mean of grouped data:

1. **State the problem:** We need to estimate the mean length of insects given grouped data with intervals and frequencies. 2. **Formula for mean of grouped data:**