### Problem 2: Analyzing Student Ages Using Cumulative Probability DistributionThe ages (to the nearest year) of students enrolled in a specific data analysis class have a cumulative probability distribution presented in the table below:| \( x \) | 17 | 18 | 19 | 20 | 21 | 22 | 23 ||--------|-----|-----|-----|-----|-----|-----|-----|| \( F(x) \) | 0 | 0.05 | 0.28 | 0.60 | 0.83 | 0.92 | 1.00 |#### Tasks:(a) **Find the mean of \( X \):**To find the mean, apply the formula for the mean of a discrete random variable using the cumulative distribution:\[\text{Mean} = \sum (x_i \cdot p_i)\]where \( p_i = F(x_i) - F(x_{i-1}) \).(b) **Find the standard deviation of \( X \):**First, calculate the variance using the formula:\[\text{Variance} = \sum (x_i^2 \cdot p_i) - (\text{Mean})^2\]where \( p_i = F(x_i) - F(x_{i-1}) \).Finally, the standard deviation is the square root of the variance.

Answer: - Given, Cumulative probability distribution function x 17 18 19 20 21 22 23 F(x) 0…

Answered: 2. The ages (to the nearest year) of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

Empirical research on stock market data for two consecutive trading days indicates that 50%% of the stocks that went up on the first day also went up on the second day. Yesterday, 400 stocks went up. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where p gives the proportion of the 400 stocks that went up yesterday that will go up today. (b) Find the standard deviation of p. (c) Compute an approximation for Pp<0.52), which Is the probability that fewer than 52 % of the stocks that went up yesterday will go up again today. Round your answer to four decimal places.
Today, the waves are crashing onto the beach every 6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 6 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is ? b. The standard deviation is ? c. The probability that wave will crash onto the beach exactly 4.2 seconds after the person arrives is P(x = 4.2) = ?
Empirical research on stock market data for two consecutive trading days indicates that 60% of the stocks that went up on the first day also went up on the second day. Yesterday, 600 stocks went up. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where p gives the proportion of the 600 stocks that went up yesterday that will go up today. (b) Find the standard deviation of p. (c) Compute an approximation for P(p > 0.56), which is the probability that more than 56% of the stocks that went up yesterday will go up again today. Round your answer to four decimal places.
Assume that adults have IQ scores that are normally distributed with a mean of 96.1 and a standard deviation of 18.1. Find the probability that a randomly selected adult has an IQ greater than 129.0. The probability that a randomly selected adult from this group has an IQ greater thanb 129.0 is (Round to four decimal places as needed.)
The lifetime risk of developing pancreatic cancer is about one in 78 (1.28%). Suppose we randomly sample 200 people. Let X = the number of people who will develop pancreatic cancer. b. Using the formulas, calculate the (i) mean and (ii) standard deviation of X. c. Use your calculator to find the probability that at most eight people develop pancreatic cancer d. Is it more likely that five or six people will develop pancreatic cancer? Justify your answer numerically.
Assume that adults have IQ scores that are normally distributed with a mean of μ=105 and a standard deviation σ=20. Find the probability that a randomly selected adult has an IQ between 93 and 117.
The random variable x represents the number of boys in a family of three children. Assuming that boys and girls are equally likely, find the mean and standard deviation for the random variable x P(x) 0.125 0.375 2. 0.375 0.125 3. OA. mean: 1.50; standard deviation: 0.76 OB. mean: 2.25, standard deviation: 0.76 OC. mean: 1.50; standard deviation: 087 OD. mean 2.25, standard deviation 0 87 Click to select your anewer Type here to search 4.
Suppose that the weight of an newborn fawn is Uniformly distributed between 2.2 and 3.9 kg. Suppose that a newborn fawn is randomly selected. Round answers to 4 decimal places when possible. The mean of this distribution is . The standard deviation is . The probability that fawn will weigh exactly 2.5 kg is P(x=2.5)=P(x=2.5)= . The probability that a newborn fawn will be weigh between 2.6 kg and 3.7 kg is P(2.6<x<3.7)=P(2.6<x<3.7)= . The probability that a newborn fawn will be weigh more than 3.24 kg is P(x>3.24)=P(x>3.24)= . P(x>2.8∣x<3.3)=P(x>2.8∣x<3.3)= . Find the 45th percentile. kg
Today, the waves are crashing onto the beach every 5.3 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.3 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 3.3 seconds after the person arrives is P(x = 3.3) = d. The probability that the wave will crash onto the beach between 1.9 and 2.3 seconds after the person arrives is P(1.9 3.26) = f. Find the minimum for the upper quartile. seconds.
Today, the waves are crashing onto the beach every 4.5 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 4.5 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 1.7 seconds after the person arrives is P(x = 1.7) = d. The probability that the wave will crash onto the beach between 1.5 and 3.9 seconds after the person arrives is P(1.5 1) = f. Find the maximum for the lower quartile. seconds.
A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter of blood. After a 12-hour fast, the random variable x will have a distribution that is approximately normal with μ = 85 and σ = 25. After 50 years of age, both the mean and standard deviation tend to increase. What is the probability that, for an adult under 50 years old, after a 12-hour fast, x is less than 130?
Today, the waves are crashing onto the beach every 5.6 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.6 seconds. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that wave will crash onto the beach exactly 0.7 seconds after the person arrives is P(x = 0.7) = d. The probability that the wave will crash the beach between 1.6 and 5.1 seconds after the person arrives is P(1.6 3.72) = f. Suppose that the person has already been standing at the shoreline for 0.8 seconds without a wave crashing in. Find the probability that it will take between 1.4 and 3.3 seconds for the wave to crash onto the shoreline. g. 65% of the time a person will wait at least how long before the wave crashes in? seconds. h. Find the minimum for the upper quartile. seconds.

SEE MORE QUESTIONS

Recommended textbooks for you

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

MATLAB: An Introduction with Applications

Statistics

ISBN:

9781119256830

Author:

Amos Gilat

Publisher:

John Wiley & Sons Inc

Probability and Statistics for Engineering and th…

Statistics

ISBN:

9781305251809

Author:

Jay L. Devore

Publisher:

Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…

Statistics

ISBN:

9781305504912

Author:

Frederick J Gravetter, Larry B. Wallnau

Publisher:

Cengage Learning

Elementary Statistics: Picturing the World (7th E…

Statistics

ISBN:

9780134683416

Author:

Ron Larson, Betsy Farber

Publisher:

PEARSON

The Basic Practice of Statistics

Statistics

ISBN:

9781319042578

Author:

David S. Moore, William I. Notz, Michael A. Fligner

Publisher:

W. H. Freeman

Introduction to the Practice of Statistics

Statistics

ISBN:

9781319013387

Author:

David S. Moore, George P. McCabe, Bruce A. Craig

Publisher:

W. H. Freeman

SEE MORE TEXTBOOKS

2. The ages (to the nearest year) of students enrolled in a specific data analysis class have a cumulative probability distribution given by 17 18 19 20 21 22 23 0.60 0.83 0.92 1.00 F(x) 0 0.05 0.28 (a) Find the mean of X. (b) Find the standard deviation of X.