# 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.#### Number of problems found: 39

- 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? - 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? - 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? - 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 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? - 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? - 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 - 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 - Lifespan

The lifetime of a light bulb is a random variable with a normal distribution of x = 300 hours, σ = 35 hours. a) What is the probability that a randomly selected light bulb will have a lifespan of more than 320 hours? b) To what value of L hours can the la - Ball bearings

One bearing is selected from the shipment of ball bearings. It is known from previous deliveries that the inner bearing radius can be considered a normal N distribution (µ = 0.400, σ2 = 25.10^−6). Calculate the probability that the selected radius will ex - A biologist

A biologist knows that the average length of a leaf of a certain plant is 4 inches. The standard deviation of the population is 0.6 inches. A sample of 20 leaves of that type of plant given a new type of plant food had an average length of 4.2 inches. At - Three sigma rule

The height of trees in a given stand is known to be a quantity with a normal probability distribution with a mean value of 15 m and a variance of 5 m². Determine the interval in which there will be tree heights in such a stand with a probability of 90% - Decides

Decide by calculation how many candidates out of a total of 1000 candidates for the position of CEO meet the eligibility requirements for the desired performance of this top management position with at least 67% probability - provided, of course, that the - Normal distribution GPA

The average GPA is 2.78, with a standard deviation of 4.5. What are students at the bottom of the 20% having what GPA? - 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

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