📊 statistics

1. **Problem Statement:** You have a dataset of 40 survey responses and want to verify if your method to calculate the standard deviation is correct. 2. **Mean Calculation:** The m

1. **Problem Statement:** Calculate the expected value $E(X)$ and the standard deviation $\sigma$ for a binomial random variable $X$ with parameters $n=10$ and $p=0.94$.

1. **Problem Statement:** We have a sample of 10 workers chosen at random from a university where 94% of workers belong to the union. We want to find: (a) The expected number of un

1. **Problem Statement:** We have a machine that produces defective pistons with probability $p=0.03$. A random sample of $n=90$ pistons is taken. We want to find:

1. **State the problem:** We have the dataset: 11, 12, 9, 11, 10, 11, 13, 10, 12. We need to compute the mean and standard deviation, then calculate the test statistic and p-value

1. The problem is to calculate the correlation coefficient $\rho$, which measures the strength and direction of a linear relationship between two variables. 2. The formula for the

1. **Problem statement:** We need to find probabilities involving the chi-square ($x^2$) distribution with given degrees of freedom (d.f.). The chi-square distribution is used in s

1. The problem is to understand how to create and interpret a scatter diagram, which is a graphical representation of two variables to identify any relationship between them. 2. A

1. The problem is to correct the frequency of the third group to 10. 2. Frequency refers to how often a particular group or event occurs.

1. The problem asks to find the mean given a total frequency of 39. 2. To find the mean, we need the sum of all data values (\( \sum f x \)) and the total frequency (\( \sum f \)).

1. **Problem Statement:** We are given monthly household incomes and need to (a) group them into class intervals of 10,000 and create a frequency distribution table, (b) compute me

1. **Problem Statement:** Find the proportion of the area under the standard normal curve for the given intervals in terms of standard deviations ($\sigma$) from the mean. 2. **For

1. **Stating the problem:** We are working with the standard normal distribution, which has mean $\mu=0$ and standard deviation $\sigma=1$. We use the Z-score formula to convert an

1. **Problem Statement:** Find the proportion of the area under the standard normal curve for the given intervals in terms of standard deviations ($\sigma$) from the mean. 2. **For

1. **Stating the problem:** We are given a set of data values and asked to organize them into a frequency distribution using the provided class intervals: 45-52, 53-60, 61-68, 69-7

1. **Stating the problem:** We have sales data $Y_t$ and price data $X_t$ for 25 quarters. We want to find the linear regression function $\hat{Y} = \hat{a} + bX_t$, the coefficien

1. **Stating the problem:** We are given a list of numbers representing the number of customers waiting at different times: $$6, 6, 6, 6, 7, 7, 5, 3, 5, 5, 3, 6, 7, 3, 6, 5, 7, 4,

1. **State the problem:** We have data on the number of customers waiting at a restaurant over 30 Saturdays. We need to create a cumulative frequency table for the number of custom

1. **Problem a (Hikers between 8 and 18 miles):** We want to find the minimum number of hikers who walked between 8 and 18 miles.

1. Problem 16 asks to determine the type of reasoning applied in the argument: "The first ball I picked from a box is green. The second ball I picked from the box is green. Therefo

1. The problem is to determine whether each given statement about normal distribution, hypothesis testing, and probability is ALWAYS, SOMETIMES, or NEVER true. 2. Let's analyze eac