Normal distribution - practice problems
It is used for random variables that are the sum of a large number of independent or only weakly dependent values. The probability distribution has a bell-shaped Gaussian curve. It is symmetric around the mean value μ, both median and mode. Three sigma rule (sigma σ = standard deviation): 68.26% of the probability belongs to the mean value μ to the distance σ, 95.45% belongs to 2σ, 99.73% to 3σ.Direction: Solve each problem carefully and show your solution in each item.
Number of problems found: 60
- 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 - A merit scholarship
Last year’s freshman class at Big State University totaled 5,307 students. Of those, 1,264 received a merit scholarship to help offset tuition costs during their freshman year (although the amount varied per student). The amount a student received was N($ - 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?
- 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.
- 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.
- 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? - 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
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