📊 statistics

1. The problem asks for the probability that a standard normal variable $Z$ lies between $-2.59$ and $1.47$, i.e., $P(-2.59 < Z < 1.47)$. 2. For a standard normal distribution, pro

1. The problem asks for the area under the standard normal curve to the left of $z = -1.42$. 2. The standard normal distribution is a normal distribution with mean $\mu = 0$ and st

1. The problem asks to find the value of $k$ such that the area to the right of $k$ under the standard normal curve is $P(z > k) = 0.0096$. 2. This means we want to find the $z$-sc

1. The problem asks to find the value of $k$ such that the area to the right of $k$ under the standard normal curve is $P(z > k) = 0.0096$. 2. This means we want to find the $z$-sc

1. The problem asks for the area under the standard normal curve to the right of $z = -2.43$. 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 4.

1. **Problem Statement:** Calculate the harmonic mean $H$ using the formula $$H = \frac{\sum f}{\sum f \left(\frac{1}{x_i}\right)}$$ where $f$ is the frequency and $x_i$ is the mid

1. **State the problem:** We have a frequency distribution table for test marks with marks 4, 5, and 8, and frequencies 2, 4, and $n$ respectively. The mean mark is given as 6. We

1. The problem: Understand what standardisation means and how to apply it in problems. 2. Standardisation is a process used in statistics to transform data so it has a mean of 0 an

1. **Stating the problem:** We have a survey of 75 people with age and food preference data. We want to find how many people aged 25 or less like both spicy and sweet food.

1. The problem is about constructing histograms, either separately or together. 2. Histograms are graphical representations of data distribution, showing frequency of data interval

1. You asked to see a picture of histograms. 2. Histograms are graphical representations of data distribution, typically shown as bars.

1. **Problem Statement:** We have marks scored by 40 pupils in English and Mathematics tests grouped into intervals. We need to: (a) Draw two histograms on the same axes for Englis

1. **Problem statement:** We have a dataset with variables $x$ and $y$. We want to fit both a linear model and a quadratic model to the data, then calculate the difference between

1. **Problem statement:** We have a normally distributed variable $X$ with mean $\mu = 30$ and standard deviation $\sigma = 4$. We want to find probabilities for different ranges o

1. **Problem statement:** We have a sample of growing stock volumes (in m^3/ha) from randomly arranged sample plots: 803, 682, 347, 808, 664, 472, 613, 199, 403, 564, 267, 396. We

1. **State the problem:** We have a sample of growing stock volumes (in m^3/ha) from randomly arranged sample plots: -803, -682, -347, -808, -664, -472, -613, -199, -403, -564, -26

1. **State the problem:** We have a sample of growing stock volumes (in m^3/ha) from randomly arranged sample plots: -803, -682, -347, -808, -664, -472, -613, -199, -403, -564, -26

1. **Problem Statement:** We need to perform three linear regressions using the dataset of countries with variables: Surface Area (independent variable), Population, and Sex Ratio

1. **State the problem:** We want to determine who performed better relative to their class by comparing Lisa's and Kevin's scores using z-scores. 2. **Formula for z-score:**

1. The problem asks to find the values of $z_1$ and $z_2$ such that the area under the standard normal curve between $z_1$ and $z_2$ is 0.8812. 2. The standard normal distribution