# 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: 52

- 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? - The usage

The usage time of the battery installed in a particular smartphone has a Normal distribution with a mean of 25.2 hours and standard deviation of 7.5 hours. What is the probability of usage time greater than 32? - Distribution 67074

The time required to complete the test has a normal distribution with a mean of 50 minutes and a standard deviation of 10 minutes. What percentage of students take the test within 30 minutes? - 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 - 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? - Life expectancy

The life expectancy of batteries has a normal distribution with a mean of 350 minutes and a standard deviation of 10 minutes. What is the range in minutes 68% of the batteries will last? What is the range in minutes? How long will approximately 99.7% of b - An insurance

An insurance company receives, on average, two claims per week from a particular factory. Assuming that a Poisson distribution can model the number of claims, find the probability it receives. three claims in a given week, more than four claims in a given - The probability

The probability that a life bulb will have a lifetime of more than 682 hours is 0.9788. The probability that a bulb will have a lifetime of more than 703 hours is 0.0051. Find the probability that a bulb will last for more than 648 hours. - Distribution 6282

The waiting time in the buffet is governed by the normal distribution with a mean value of 130 seconds and a variance of 400. What is the probability that someone will wait less than a minute and a half? - 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 - 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. - 10km race

Joan's finishing time for the bolder boulder 10 km race was 1.77 standard deviations faster than the women in her age group. 415 women ran in her age group. Assuming a normal distribution, how many women ran more quickly than Joan? - Two sigma

Khail took his math test and scored 88. If the class average was 78 with a standard deviation of 5, what percent of students earned a higher grade than Khail's grade? - Distribution 81063

The weight of a loaf of bread should be 900 g. Loaves whose weight differs by more than 30 g from this value must be rejected. Determine the probability that a loaf is rejected if its weight has a normal distribution N(900,40). - Distribution 6283

The life of the bulbs has a normal distribution with a mean value of 2000 hours and a standard deviation of 200 hours. What is the probability that the light bulb will last for at least 2100 hours? - 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 - 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. - Distributions 82068

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 - An exam - normal distribution

Five thousand students take an exam with a mean of 59 and a deviation of 8. How many students will score less than 75? - 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?

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