# Mean and Standard Deviation of a Probability Distribution

Understanding the mean and standard deviation of a probability distribution is fundamental in statistical analysis. The mean, often referred to as the expected value, provides a measure of central tendency, indicating the average outcome. Meanwhile, the standard deviation quantifies the dispersion or spread of the distribution around the mean, offering insights into the variability of the data. Together, these statistical measures enable researchers and analysts to assess the central tendency and variability of a dataset, facilitating informed decision-making and drawing meaningful conclusions from the data.

Questions

- You keep track of the time you spend doing homework each evening. You spend 58 minutes, 36 minutes, 44 minutes, and 37 minutes. How do you find the mean of these times?
- How do you find the mean of the following set of numbers: 12, 14, 16, 12, 13?
- The commuting time for all employees of a company has a normal distribution with a mean of 44.6 minutes and a standard deviation of 11.2 minutes. What is the probability that the mean computing time by a sample of 12 employees is between 43.26 and 49.35?
- What is the standard deviation of {44, 46, 33, 10, 50, 27}?
- A student received grades of 99, 81, 86, and 81 on math quizzes. How do you find the student's average?
- What is the average of 14, 29 and 142?
- What are the mean and standard deviation of the probability density function given by #(p(x))/k=ln(x^3+1)# for # x in [0,1]#, in terms of k, with k being a constant such that the cumulative density across the range of x is equal to 1?
- The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. The probability of a player weighing more than 241.25 pounds is?
- Find the standard deviation for the data set. 35,36,36,38,41,42,45,48?
- What are the mean and standard deviation of a binomial probability distribution with #n=9 # and #p=11/32 #?
- A continuous random variable X has the p.d.f. F(x)={Ax(6-x)² if 0<x<6 ,{0 if otherwise Calculate the mean and standard deviation of X.Construct the distribution function F(x) and hence evaluate P(X>1/4).?
- What are the mean and standard deviation of a binomial probability distribution with #n=11 # and #p=7/30 #?
- On a standard measure of hearing ability the mean is 300 and the standard deviation is 20. What is the z-score for a person who scores 340?
- The mean of a set of data is 4.11 and its standard deviation is 3.03. What is the z-score for a value of 10.86?
- Brock scored the following number of goals in her soccer games: 2, 3, 1, 0, 3, 2,1, 2. What is the mean of the data?
- The average weight of 6 students is 62 kg. If a 7th student weighs 52 kg, what is the new average weight of all 7 students?
- The grade point averages for 10 randomly selected junior college students are 2.0, 3.2, 1.8, 2.9, 0.9, 4.0, 3.3, 2.9, 3.6, 0.8. Assume the grade point averages are normally distributed. What is the 98% confidence interval for the true mean?
- What are the mean and standard deviation of a binomial probability distribution with #n=5 # and #p=4/7 #?
- What are the mean and standard deviation of the probability density function given by #p(x)=ke^-x # for # x in [0,1]#, in terms of k, with k being a constant such that the cumulative density across all x is equal to 1?
- What are the mean and standard deviation of a binomial probability distribution with #n=120 # and #p=3/4 #?