### Probabilities of School-Related Extracurricular ActivitiesThe given data represents the probability distribution of the number of school-related extracurricular activities per student.#### Activities and their Probabilities:| Activities (X) | Probability (P(X)) ||----------------|---------------------|| 0 | 0.057 || 1 | 0.124 || 2 | 0.164 || 3 | 0.178 || 4 | 0.210 || 5 | 0.128 || 6 | 0.086 || 7 | 0.053 |---### Calculating Statistical Measures**(a) Find the mean, variance, and standard deviation of the probability distribution.**1. **Mean (μ)**: - Sum of (X * P(X)) for all values of X. - The mean is ___ (Round to one decimal place as needed).2. **Variance (σ²)**: - Sum of [(X - μ)² * P(X)] for all values of X. - The variance is ___ (Round to one decimal place as needed).3. **Standard Deviation (σ)**: - Square root of the variance. - The standard deviation is ___ (Round to one decimal place as needed).---**(b) Interpret the results:**- The mean is ___, so the average student is involved in ___ extracurricular activities.- The standard deviation is ___, so the typical number of activities per student is distributed around the average with a deviation of ___. (Round to one decimal place as needed).

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Answered: (a) Find the mean, variance, and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Using the image answer the following. Find the probability that a randomly selected household in North America uses between 69 and 161 gallons of water per day. Show work
The purpose of this assignment is to check that you are able to properly use the statistical keys on your calculator to find the mean and standard deviation. The data below represents the number of siblings that each student has in a random sample of 10. Enter the data into your calculator, then find the mean and standard deviation. Express each to the tenths place. (to one decimal place) 2 6 3 1 1 6 2 1 3 4 A. sample mean x̄ ____________ B. sample standard deviation s ____________
Rochester, New York, averagesµ = 21.9 inches of snow for the month of December. The distribution of snowfall amounts is approximately normal with a standard deviation of σ =6.5 This year, a local jewelry store is advertising a refund of 50% off of all purchases made in December, if Rochester finishes the month with more than 3 feet (36 inches) of total snowfall. What is the probability that the jewelry store will have to pay off on its promise?
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Suppose the scores of students on a Statistics course are Normally distributed with a mean of 596 and a standard deviation of 33.What percentage of the students scored between 596 and 662 on the exam? (Give your answer to 3 significant figures.)_________%
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A standardized exam's scores are normally distributed. In a recent year, the mean test score was 1533 and the standard deviation was 313. The test scores of four students selected at random are 1950, 1290, 2220, and 1440. Find the z-scores that correspond to each value and determine whether any of the values are unusual. The Z-score for 1950 is. (Round to two decimal places as needed.)
Which of the statements below is true about the standard error of the sampling distribution of the sample mean. It measures the variabilty of the mean from sample to sample. It is less than the standard deviation of the population. All of the above. It decreases as the sample size increases.
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 206.8 cm and a standard deviation of 0.5 cm. Find the probability that the length of a randomly selected steel rod is greater than 208.4 cm. P(x > 208.4 cm) = P(z > Shade: Left of a value Click and drag the arrows to adjust the values. -4 -3 -2 -1 2. -1.5
Your Turn: Standardized Scores Scores on the final exam in Ms. Meyer's statistics class follow a normal distribution, with a mean of 82 and a standard deviation of 5. 1. Ron, who took Ms Meyer's class, scored 88 on the final. Ron's z-score is Click to view hint 2. This means that Ron's final score is Click to view hint 3. Dan also took Ms. Meyer's class, and the z-score of his final is -2.4. This means that Dan's score is: Click to view hint 4. Dan's actual score on the final is Click to view hint 5. Julie was assigned to take her statistics class with Mr. Fisher, whose final scores followed normal distribution with mean 75 and standard deviation of 6. Her score on the final was 84. Which of the two scores, Ron's or Julie's, is more impressive? Click to view hìnt Check
Suppose in 2000, the science scores for female students had a mean of 146 with a standard deviation of 35. Assume that these scores are normally distributed with the given mean and standard deviation. _________________ of the female students scored between 76 and 216

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