Math Problem Statement

What is the Normal Distribution Probability where X is more than 185.61 for a mean of 206, and standard deviation of 20.6

integer, decimal, or E notation allowed

Question 10

1 Point

Calculate the standard deviation sales per store using this population data

91, 53, 71, 4, 30, 16

Integer, decimal, or E notation allowed

I

Question 11

1 Point

Calculate the median for products sold per store using this data.

0, 77, 38, -5, 44, 62

Use python

Solution

Here are the results for your questions:

  1. Normal Distribution Probability (for X>185.61X > 185.61, with mean = 206 and standard deviation = 20.6):
    Probability = 0.8389 (rounded to 4 decimal places).

  2. Standard Deviation (of sales dataHere are the results for your questions:

  3. Normal Distribution Probability (for X>185.61X > 185.61, with mean = 206 and standard deviation = 20.6):
    Probability = 0.8389 (rounded to 4 decimal places).

  4. Standard Deviation (of sales 91, 53, 71, 4, 30, 16):
    Standard Deviation = 30.55 (rounded to 2 decimal places).

  5. Median (for products sold per store: 0, 77, 38, -5, 44, 62):
    Median = 41.0.

Let me know if you need further clarification or have any other questions!

Here are 5 related questions for deeper understanding:

  1. How is the Z-score used to calculate normal distribution probabilities?
  2. What is the difference between population and sample standard deviation?
  3. How does changing the mean or standard deviation affect the normal distribution curve?
  4. What are the key properties of the normal distribution?
  5. Why is the median a useful measure of central tendency, especially with outliers?

Tip: The standard deviation gives insight into the spread of data. A larger standard deviation means more variability from the mean.

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Math Problem Analysis

Mathematical Concepts

Probability Theory
Normal Distribution
Descriptive Statistics
Standard Deviation
Median

Formulas

Z-score formula: Z = (X - μ) / σ
Standard deviation formula: √(Σ(X - μ)^2 / N)
Median calculation

Theorems

Empirical Rule for Normal Distribution
Central Limit Theorem

Suitable Grade Level

Grades 10-12