[ f(x, y) = c (x^2 – y^2) hspace{0.5in} 0 leq x lt infty, hspace{0.2in} -x leq y leq x ] This question aims to find the conditional distribution of the given function with a given condition X=x. The question is based on the joint density function and conditional distribution concepts. The conditional distribution is the […]

# Category Archives: Statistics Q&A

This problem aims to familiarize us with the method of poof. The concept required to solve this problem is related to discrete mathematics, including direct proof or proof by contradiction, and proof by contrapositive. There are multiple methods to write a proof, but here we are going to see only two methods, proof by contradiction […]

The question aims to find out the p-value using the given alternative hypothesis, which is a one-sided hypothesis. Therefore, the p-value will be determined for the left tail test with reference to the standard normal probability table. When the alternative hypothesis states that a certain value for a parameter in the null hypothesis is lesser […]

### Suppose that X is a normal random variable with mean 5. If P(X>9)=0.2, approximately what is Var(X)?

This question aims to find the probability of a normally distributed random variable $X$. A random variable is one whose value is determined by the results of a statistical experiment. The normal distribution, also known as the Gaussian distribution or the z-distribution, has a mean of zero and a standard deviation of one. Data in a […]

-a) What percentage of 25-year-old men are over $6$ feet, $2$ inches tall? -b) What percentage of men in the $6$-footer club are over $6$ feet, $5$ inches? This question aims to explain the mean, variance, standard deviation, and z-score. The mean is the central or the most common value in a group of numbers. […]

This question belongs to the statistics domain and aims to understand the alpha level, confidence level, z-critical values, the term $z_{alpha /2}$ and further explains how to calculate these parameters. The alpha level or significance level is the probability of producing a false decision when the null hypothesis is correct. Alpha levels are employed in […]

– Dollars list price – $435.20$$ – Trade discount rate – $26%$, $15%$,and $5%$ The aim of this article is to find the net price factors from the given trade discount rate and use them to find the net price. The basic concept behind this article is the understanding of Item List Price, Trade Discount, […]

This problem aims to find a bunch of random numbers from a row of numerical values. The main concept behind this problem is mostly related to random numbers and their generation. Now as the phrase suggests, a random number is just a number chosen by luck. In a random number distribution, all the numbers have […]

This question aims to develop key concepts regarding the confidence intervals and the sample means which are the fundamental concepts when it comes to the application of statistics in practice, especially in data science and project management, etc. By definition, a confidence interval is basically a range of values. This range is centered on the […]

The aim of this question is to analyze the bell curve. The given curve is a perfect bell shape because, from the mean, the values are the same on both sides, i.e., on the left and right. This question is related to the concepts of mathematics. Here, we have to calculate three basic parameters: mean μ, […]

This article discusses the sample mean, standard error, and the sampling distribution of p, the random sample with a size of 100. This article uses the concept of sample mean and standard error. The sample mean is defined as the average of a set of data. Standard error is how different the population mean is from the sample mean. […]

-(a) [ alpha = 0.0089 ] -(b) [ alpha = 0.09 ] -(c) [ alpha = 0.707 ] In this question, we have to find the value of $ Z_{ alpha }$ for all the three parts where the value of $ alpha $ is given already. The basic concept behind this question is the […]

### What is an advantage of using a stem-and-leaf plot instead of a histogram? What is the disadvantage?

This question aims to resolve the advantages and disadvantages of using a stem-and-leaf plot for visualizing statistical data. Stem-and-leaf plots are used widely in visualizing the overall summary of statistical data. To develop an understanding of the core concept, let’s consider the following arbitrary data as an example: { 1, 2, 3, 4, 5, 11, […]

The objective of this question is to find the number of ways the six indistinguishable balls can be distributed into nine distinguishable bins. A mathematical method for determining the number of potential groupings in a set of objects in which the selection order becomes irrelevant is referred to as combination. The objects can be chosen […]

This question widely explains the concept of the sampling distribution of sample proportions. The population proportion plays an important role in many areas of science. This is because research questionnaires in many fields involve this parameter. The success proportion is calculated by the sampling distribution of sample proportions. It is the ratio of the chance […]

The aim of this question is to understand the key concept of a random variable using the coin toss experiment which is the most basic binomial (experiment with two possible outcomes) experiment performed in probability theory. A random variable is nothing but a mathematical formula used to describe the outcome of statistical experiments. For example, […]