Binomial distribution - practice problems - page 4 of 7
Instructions: Solve each problem carefully and provide a detailed solution for every item.Number of problems found: 133
- Car drive distribution
Five men drive to work together; 2 have a Škoda car, and the others have an Opel, Seat, and Hyundai. They always randomly choose which car to drive. Each of the five cars has an equal chance. The random variable X determines how many days the same charact - 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 Healthcare issues are receiving much attention in both academic and political arenas. A sociologist recently surveyed citizens over 60 years of age whose net worth is too high to qualify for government health care but who have no private health insurance.
- Publishing company Suppose you work for a publishing company, and before launching a new magazine targeting fashion-oriented consumers, your boss wants to hold a meeting with prospective advertisers. Assume that annual expenditures on magazine ads in this genre are normally
- Mortality tables
Mortality tables enable actuaries to obtain the probability that a person will live a specified number of years at any age. Insurance companies and others use such probabilities to determine life insurance premiums, retirement pensions, and annuity paymen - Binomial probability
What is the binominal probability that at least 4 of the six trials (n=6) are succeeded where φ = 0.50? - Phone call probability One hundred people work in the office. Each of them spends an average of 25 minutes daily on the phone. A working day has 8 hours. What is the probability that ten workers will be on the phone simultaneously in one day?
- Level of significance
At a certain college, it is estimated that 25% of the students have cars on campus. Does this seem to be a valid estimate if, in a random sample of 90 college students, 28 are found to have cars? Use a 0.05 level of significance. - Unemployment rate Over the last 16 years, the country's unemployment rate has changed according to the following frequency table: years of unemployment: 2 5 2 3 3 1 unemployment rate: 0.5 1 1.5 2 2.5 3 in % (percent). Determine the two-sided confidence interval for the var
- Poisson distribution - daisies
The meadow behind FLD was divided into 100 equally large parts. Subsequently, it was found that there were no daisies in ten of these parts. Estimate the total number of daisies in the meadow. Assume that daisies are randomly distributed in the meadow. - 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 - Dice six probability
We were tasked with throwing the dice until we hit the "six." a) Find the average number of throws we will have to make to complete the task. b) How many times do we have to roll the dice so that the probability of falling at least one "six" is at least 9 - Probability
In the elections, 2400000 voters out of a total of 6000000 voters voted for party Z. Let us randomly select three voters and consider the random variable ξ={number of voters for party Z in the sample of three voters}. Determine a) the probability distribu - Twenty
Twenty swallows sit on a 10 m long telephone cable. Assume that swallows are completely randomly distributed along the line. (a) What is the probability that more than three swallows sit on a randomly selected section of cable 1 m long? (b) What is the pr - Seeds
We randomly selected ten seeds from a box of spruce seeds with an 80% germination rate and planted them. Find the median of the random variable, the number of germinating seeds. - Statistical survey
Write TRUE OR FALSE for each question: 1 Standard deviation measures 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 data is sh - Bernoulli distribution The production of solar cells produces 2% of defective cells. Assume the cells are independent and that a lot contains 800 cells. Approximate the probability that less than 20 cells are defective. (Answer to the nearest three decimals).
- Crime solving probability
The police solved 21 crimes in the monitored period. The probability of solving a crime is 0.64. What is the probability that the police: a) just solved 7 crimes b) did not solve at least 2 criminal offenses P.S. Let's assume ideal police officers - Employee reduction probability
Seven women and 3 men work in one office. According to the new regulation, reducing the number of employees by three is necessary. In a random sample of employees, what is the probability that they will be fired: a. One woman and two men b. At least one w
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