# 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: 24

- An exam - normal distribution

5000 students take an exam with a mean of 59 and a deviation of 8. How many students will score less than 75? - 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? - Three sigma rule

Stoach weights are normally distributed, with mean 1314g and standard deviation 113g. State the probability that a randomly selected stoach weighs more than 1118g. (Report the probabilities using at least 4 decimal places. ) - Suppose 4

Suppose that 14% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be - Rich retirement

Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for government health care but who have no private hea - Performance comparing

A standardized test was administered to thousands of students with a mean score of 85 and a standard deviation of 8. A random sample of 50 students were given the same test and showed an average score of 83.20. Is there evidence to show that this group ha - 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% - A machine

A machine produces steel rods of normally distributed length; the mean length and the standard deviation being 50.0 cm and 0.5 cm respectively. The rods do not conform to safety standards if they are either shorter than 49.1 cm or longer than 50.7 cm in l - Statistical survey

Write TRUE OR FALSE for each question: 1 Standard deviation is a measure of central location. 2. The most frequent observation in a data set is known as the mode. 3 The most passive method of data collection is observation. 4 Access time for secondary dat - A mountain climber

A mountain climber plans to buy some rope to use as lifeline. Which of the following would be the better choice? Explain your choice. Rope A: Mean breaking strength:500lb; standard deviation of 100lb Rope B: Mean breaking strength: 500lb; standard deviati - Tallest people a

As a group, the Dutch are amongst the tallest people in the world. The average Dutchman is 184 cm tall. If a normal distribution is appropriate, and the standard deviation for Dutchmen is about 8 cm, what is the percentage of Dutchmen who will be over 2 m - Statistics quiz

Fill in the missing word 1. in a data set, the mean, median and mode are measured of ________________ 2. "The manipulation of variables under controlled conditions"is the data collection method known as______________ 3. in a normal distribution, the area - IQ Intelligence quotient

Intelligence quotient (IQ) is a standardized score used as the output of standardized intelligence psychological tests to quantify a person's intelligence with the rest of the population (respectively to a given group). Intelligence has an approximately n - Assembly time

The assembly time for the toy follows a normal distribution with a mean of 75 minutes and a standard deviation of 9 minutes. The company closes at 5 pm every day. If one starts assembling at 4 pm what is the probability that he will finish before the comp - Stoaches

Stoaches are fictional creatures distantly related to bigfoot and yeti. Stoach weights are normally distributed, with mean 904g and standard deviation 104g. State the probability that the sample mean of a random sample of 36 stoach weights exceeds 943g. ( - 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) Up to what value of L hours can the - 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 as a normal distribution of N (µ = 0.400, σ2 = 25.10^−6). Calculate the probability that the selected radius w - Life expectancy

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

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

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