Math Problem Statement

The original question submitted by the user includes four statistical problems involving normal distributions, frequency distributions, and data visualization tasks.

Solution

The image you uploaded contains several statistical problems in Indonesian. Here’s a breakdown and how we can approach them:

Soal 1 (25%)

Data: The weights (in kg) of 32 students are given. The task is to: a. Create a frequency distribution with class intervals. b. Create a bar chart. c. Create a stem-and-leaf plot. d. Create a box plot and analyze it.

Soal 2 (25%)

The second problem involves a city’s per capita income, which is normally distributed with:

  • Mean (μ) = Rp98,000,000
  • Standard deviation (σ) = Rp16,000,000

It asks to compute the probability of randomly selecting an individual with an income: a. Greater than Rp50,000,000. b. Greater than Rp122,000,000. c. Between Rp85,200,000 and Rp122,000,000. d. Between Rp114,000,000 and Rp130,000,000.

Soal 3 (25%)

This problem discusses a company’s sales, which follow a normal distribution with:

  • Mean (μ) = Rp2,000,000
  • Standard deviation (σ) = Rp250,000

It asks to compute: a. Probability that sales exceed Rp2,500,000. b. Probability that sales fall below Rp1,250,000. c. The minimum sales to cover fixed costs (Rp1,450,000), and whether it’s probable to exceed this. d. Determine the highest sales level likely to be surpassed in the future.

Soal 4 (25%)

The fourth problem deals with GPA (IPK) distribution for 3500 students at FEB UNESA, which follows a normal distribution with:

  • Mean (μ) = 3.23
  • Standard deviation (σ) = 0.3

It asks to calculate: a. The percentage of students with GPA between 3.1 and 3.6. b. The total number of students with GPA below 3.0. c. The lowest GPA in the top 5% of students (for the International Class Program).


Would you like to focus on solving one of these problems first? If so, please let me know which one, and I can walk you through it with step-by-step calculations.

Relative Questions:

  1. How do you construct a frequency distribution for grouped data?
  2. What is the significance of a stem-and-leaf plot in data visualization?
  3. How do you interpret the results of a normal distribution calculation?
  4. Why is a box plot useful for analyzing data?
  5. How do you determine percentiles in a normal distribution?

Tip: When dealing with normal distributions, always note down the mean and standard deviation first, as they are key to finding probabilities and percentiles.

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Math Problem Analysis

Mathematical Concepts

Normal distribution
Frequency distribution
Stem-and-leaf plot
Box plot
Probability

Formulas

Z = (X - μ) / σ
Frequency distribution formula
Box plot quartile calculation

Theorems

Empirical Rule
68-95-99.7 Rule for normal distribution

Suitable Grade Level

College/University Level (Statistics)