Standard deviation - practice problems - page 2 of 6
The standard deviation, symbol sigma σ, is a statistical measure of the variability of a data set. Simply put, it tells us how spread out the values are around the mean (arithmetic mean). How far away most of them are from the mean. It is a non-negative number, defined as the square root of the variance of the data. It therefore has the same dimensions as the data.Variance in statistics is the average of the squares of the deviations from the mean (mean). Variance is also a non-negative number.
The sample standard deviation is defined as the square root of the sample variance. When calculating the sample variance, for n data, only (n-1) independent data are considered.
Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 114
- 3 sigma
Students' performance scores in a statistic test have a mean of 70 and a standard deviation of 4.0. The scores obtained can be modeled by a normal distribution. Find the probability that the score of a randomly selected student is i. more than 80 marks ii - The profit 3
An investment's profit (or loss) is normally distributed with a mean of $11,200 and a standard deviation of $8,250. What is the probability of a loss rather than a profit? - The Uniform Distribution
The number of tickets purchased by an individual for Beckham colleges holiday music festival is uniformly distributed random variable ranging from 5 to 12. What is the standard deviation? - Suppose 8 Suppose the scores on a test have a normal distribution with X=74 and a standard deviation of s=18. What percentage of students have scores higher than 90? What percentage of students have scores between 70 and 85? Twenty percent of the students do better
- Lifetime - bell curve
Laser lifetime follows a normal distribution with a mean of 7000 hours and a standard deviation of 600 hours. What is the probability that the laser will fail before 6000 hours? What is the probability that the laser will last at least 7500 hours? - Javelin throwers
Javelin throwers Anna and Barbora have average throw lengths of 67 m and 75 m, respectively, and standard deviations of 6 m and 3 m, respectively. Assume that the throw lengths have independent normal distributions. Calculate the probability that Anna thr - Distribution 82042
Assume that the IQ in the population follows a normal distribution with a mean of 100 points and a standard deviation of 10 points. With what probability among 15 randomly selected people: a. Is there anyone with an IQ above 130 points? b. Are there at le - Statistical 81497
Determine the median, mode, arithmetic mean, variance, standard deviation, range of variation, and coefficient of variation of the character x in the statistical file: 2x 9, 7x 10, 9x 11, 11x 15, 15x 17, 16x 19, 13x 21, 10x 25, 9x 29, 4x 32 - Confidence interval When checking the use-by date of a specific type of canned meat in warehouses of meat industry products, 340 canned goods were randomly selected, and it was found that 63 of them had passed their warranty period. Establish a 95% confidence interval to est
- Characteristics: 80608 Arithmetic mean xA=40 and standard deviation sx=8 were calculated. Determine from which numbers the student calculated the given characteristics: a) 24 and 56 b) 16 and 64 c) 32 and 48
- Entrance exam In a college entrance exam, the participants are rated as excellent, very good, good, and fair. Consider that the scores in the exam are normally distributed with a mean of 78 and a standard deviation of 7.5. The participants receiving the top 5% of the s
- IQR and range The times spent in minutes by 20 people waiting in a queue at the bank for a teller were: 3.4, 2.1, 3.8, 2.2, 4.5, 1.4, 0,0, 1.6, 4.8, 1.5, 1.9, 0, 3.6, 5.2, 2.7, 3.0, 0.8, 3.8, 5.2, Find the range and interquartile range of the waiting times.
- Z score transformation Suppose a distribution has a mean µ = 8 and standard deviation σ = 4. What is the value of x if it is z = +1.50?
- Normally distributed
Suppose the height of male youngsters is normally distributed with a mean of 60 inches and a standard deviation of 10. what percentage of the boy's height would we expect to be between 44 and 75, less than 49, and 76 and more?
- The average 7 The average lifespan for cricket is 90 days, with a standard deviation of 13 days. If we assume that the lifespan of cricket is normally distributed, a. What is the probability a randomly selected cricket has a lifespan of fewer than 75 days? b. What is t
- Dataset 3
Given dataset: 31, 28, 31,30,31,30,31,31,30,31,30,31 1. Construct a frequency table. 2. Construct a histogram. 3. Compute the mean. 4. Compute the median. 5. Find the mode. 6. Compute the midrange. 7. Compute the standard deviation. - Quartile statistics Use the following data, which was obtained from a study of weights of adult men, to answer problems: Mean ; 192 lb ; First quartile ; 178lb Median; 185lb ; Third quartile ; 232 lb Mode ; 180 lb ; 86th percentile ; 239 lb Standard Deviation ; 23lb; ; a) Wh
- Z-score test
The fish weights in a certain lake are normally distributed with a mean of 11 lb and a standard deviation of 6. If four fish are randomly selected, what is the probability that the mean weight will be between 8.6 and 14.6 lb? Your answer should be a decim - Summaries A specialist teacher observes the time taken by each of the students with learning disabilities to complete a psychological task. She summaries the times using the following: Time Taken(mins) ; 1-5; 6-10; 11-12; 16-20 No. of Student ; 2 ; 4 ; 12; 4 Using
A sample of 10 randomly selected students revealed the following grades in Business Statistics first test (on a marking scale of 0 to 100): 79, 63, 60, 45, 55, 58, 59, 62, 40, 68. Examine the data using groups and presenting: a) the Histogram of the absolDo you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
