### Problem 3: Analyzing Probability Distributions**Task:** Determine the following from the graph. Show all your work.#### a) Determine the Mean and Standard Deviation:The image includes a graph titled **"PDF of a Random Variable."** The graph appears to be a bell-shaped curve, typical of a **normal distribution.** The x-axis ranges from 0 to 60, while the y-axis represents probability density.To find the mean and standard deviation from the graph, look for the peak of the curve, which indicates the mean. The spread of the curve provides information about the standard deviation.#### b) Draw a Qualitative Sketch of the CDF:You are tasked with drawing a qualitative sketch of the **Cumulative Distribution Function (CDF)** based on the given Probability Density Function (PDF). - The CDF should start at 0 on the y-axis at the far left of the x-axis and increase to 1 at the far right.- Key points, such as inflection points and the mean, should be noted.#### c) Type of Distribution:The shape of the PDF strongly suggests it is a **normal distribution**. - **Answer for c):** Normal DistributionWhen analyzing distributions, it is essential to understand these concepts as they provide foundational insights into data behavior and probabilistic outcomes.

Answered: 3. Determine the following from the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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please answer question 2 below
Question 3 Match the questions with answers. Use this sample data for all questions: Table 2: Time taken in seconds. Sample 290, 340, 150, 300, 200, 100, 400, 500, 600, 89, 94 What is the mean for table 2? A. 278.45 What is the median for table 2? B. no mode v What is the mode for table 2? C. 172.06 v What is the sample standard deviation for table2 ? D. -0.46 Calculate the 75th percentile for table 2. E. 622.58 v What is the interquartile range for table 2? F. 290.00 What is the z score for an x value of 200 using table 2? G. 0.46 v Using the empirical rule to find the range of values containing 95% of the data from table 2, what is the upper value of the range? Hint: use the mean and standard deviation you previously calculated. H. 794.64 I. 177.95 J. 400.00 K. 300.00 L. 198.38 M. 100 N. 370

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