Standard deviation - practice problems
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.
Task: Work through each problem with care and demonstrate your solution process for each one.
Number of problems found: 119
- Lightbulbs
The physical plant at the main campus of a large state university recieves daily requests to replace fluorescent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 48 and a standard deviation of 10. Using the emp - The airlines
The airline's company is interested in decreasing the waiting time spent by customers while buying air tickets. So, the relationship between waiting time "y" in minutes and the number of counters "x" operating to sell tickets has been studied (Marks 6) Th - A random 2
A random sample of 40 families has an average water consumption of 29 cubic meters per month, with a sample standard deviation of 8 cubic meters. Give the 90% confidence interval for the mean usage of water per month. - Fish service
According to a report by the U. S. Fish and Wildlife Service, the mean length of six-year-old rainbow trout in the Arolik River in Alaska = 484.6 millimeters with a standard deviation = 31.2 millimeters. Assume these lengths are normally distributed. What - Bell curve A company has a policy of retiring company cars; this policy looks at the number of miles driven, purpose of trips, style of car, and other features. The distribution of the number of months in service for the fleet of cars is bell-shaped and has a mean o
- IQ scores
IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What percentage of the population scores higher than 125 on an IQ test? - The usage The battery usage time installed in a particular smartphone has a Normal distribution with a mean of 25.2 hours and a standard deviation of 7.5 hours. What is the probability of usage time greater than 32?
- Squared deviation
Given the data from the problem (sample data: 23, 27, 35, 44), find the sum of the squared deviations (the numerator of the fraction under the square root in the formula). In finding the number, round all calculations to 2 decimals (if you carry more or f - Suppose 12
Suppose in a physics test involving 30 students, and four scored 75%, eight scored 60%, twelve scored 50%, and six scored 30%. Calculate the mean of the group and the standard deviation. - The mass 3
The mass of certain types of cabbage is normally distributed with a mean of 1000 g and a standard deviation of 0.15 kg. In a batch of 800 cabbages, estimate how many a mass between 750g and 1290g. - Coefficient of skewness For the data set whose Karl Pearson's Coefficient of skewness = -2.25, variance is 16, and Mean is 35, then its median value will be:
- A sample variance
Calculate the value of the sample variance. −8,−8,−3,13,4,−8,10,8 - Compare variation The mean blood pressure was 135 mmHg in a series of adults with a standard deviation of 10 mm Hg. In the same series, the mean height was 170 cm with a standard deviation of 6 cm. Find which character shows a greater variation (write A or B).
- Q10 - investigate A nutritionist who investigates fruits reported that the average weight of a raspberry is 4.4 g with a standard deviation of 1.28 g. What is the probability that a randomly selected raspberry would weigh less than 3.1 grams? Let X represent the weight of
- A random
A random sample of 225 nails in a manufacturing company is gathered. The engineer specified that the specified length of a nail must be 8 cm having a standard deviation of 0.04 cm. It shows from the sample that the average length of the nails is 8.055 cm. - The number 7 The number of faulty units in a carton of a particular product is known to be normally distributed with a Mean of 10 and a variance of 25. What portion of a given carton of the product is expected to contain___ faulty units? (I) less than 8 (ii) more than
- Lengths 6 Lengths of 130 tubes are measured. The arithmetic mean is 17.27 cm, and the standard deviation is 1.2 cm. How many tubes do have a length: a) between 16.5 cm and 18.1 cm b) greater than 17 cm
- Bulb life
Tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. Find the probability that a randomly selected light bulb will last between 675 and 900 hours. - Z-score calc
What is the Z Score for the following numbers: X is 16, and data for the population mean, and the standard deviation is 196, 193, 79, 30, 29, 81, 25, 21, 164 Level of difficulty = 2 of 2 Please format it to 2 decimal places. - Z-score 3 A random variable X has a mean of 4 and a standard deviation of 2. What is the corresponding z-score for x = 7?
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