📊 statistics

1. **State the problem:** We have 70 numbers with different values and frequencies: 15 numbers are 60, 10 numbers are 75, 12 numbers are 55, 9 numbers are 65, and the rest are 80.

1. **Stating the problem:** We are given a table with values of a random variable $x$ and their probabilities $p(x)$, and we want to calculate the variance and standard deviation.

1. **State the problem:** We want to test the marketing manager's claim that the average monthly data usage of prepaid customers is 5 GB based on a sample of 50 customers with mean

1. **Problem 1:** Find the probability that a child picked at random has a height greater than 104cm. Given: $X=104$, $\mu=110$, $\sigma=5$

1. **Problem statement:** Find the probability that a child picked at random has a height greater than 104cm. Given: $X=104$, $\mu=110$, $\sigma=5$

1. **Problem:** Find the probability $P(-0.73 < Z < 0.63)$ where $Z$ is a standard normal variable. 2. **Formula and rules:** For a standard normal distribution, probabilities betw

1. **Problem:** Find the probability $P(-0.73 < Z < 0.63)$ where $Z$ is a standard normal variable. 2. **Formula and rules:** For a standard normal variable $Z$, the probability be

1. The problem is to round up the percentile rank given as 4. 2. Rounding up means increasing the number to the nearest integer greater than or equal to the number.

1. **Problem Statement:** (a) Find the percentile rank for score 20 in the given set of 30 exam scores.

1. **Stating the problem:** We have raw scores of 150 applicants for an interview in Computer Technology and need to represent this data using a bar graph. 2. **Understanding bar g

1. **Problem statement:** We have a set of 30 exam scores and need to find the percentile ranks for scores 20 and 68.

1. **State the problem:** We want to perform an independent samples t-test to compare the means of two groups: April (in glasses) and January (in glasses). 2. **Formula for indepen

1. **Problem Statement:** We have a frequency distribution table of Subjective Happiness scores for 200 students. We need to complete the missing columns: Real limits, Median, Freq

1. The problem is to draw a graph of the standard normal distribution, plot a specific z-score, and shade the area corresponding to that z-score. 2. The standard normal distributio

1. **Problem statement:** We have a normally distributed variable representing cholesterol content in a cup of ice cream with mean $\mu = 660$ mg and standard deviation $\sigma = 3

1. **Problem statement:** We have a normally distributed variable representing cholesterol content in a cup of ice cream with mean $\mu = 660$ mg and standard deviation $\sigma = 3

1. **Find the median for each set of data.** Median is the middle value when data is ordered from least to greatest. If there is an even number of data points, median is the averag

1. **State the problem:** Find the mode of the numbers $1, 2, 4, 6, 4$. 2. **Definition:** The mode is the number that appears most frequently in a data set.

1. **Problem statement:** Find the quadratic regression equation $\hat{y}_x = A x^2 + B x + C$ and the sample correlation ratio $n_{yx}$ based on the given frequency table.

1. **Problem statement:** We want to find the lower and upper systolic blood pressure readings that include the middle 75% of the population, assuming a normal distribution with me

1. **State the problem:** We are testing the hypothesis about the population mean $\mu$ with null hypothesis $H_0: \mu = 10$ and alternative hypothesis $H_a: \mu > 10$ at significa