# Binomial distribution + probability - math problems

#### Number of problems found: 45

• Population variance In a California community college, 60% of students will transfer to a college in the CSU system. The number of students in a sample who will transfer follows a binomial distribution. If 8 students are randomly selected, find the population variance σ2 of
• Sample Proportion In a California community college, 60% of students will transfer to a college in the CSU system. The number of students in a sample who will transfer follows a binomial distribution. 400 students are randomly selected from the college and 224 of them will
• Error rate The exam has 6 questions. Students have an error rate of 20% and can have a maximum of 1 question wrong. What is the probability that they will succeed?
• 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
• Mortality tables Mortality tables enable actuaries to obtain the probability that a person at any age will live a specified number of years. 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 6 trials (n=6) are succeeded where φ = 0.50?
• 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 l
• 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 From a box of spruce seeds with the germination of 80%, we randomly select 10 seeds and plant 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 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
• 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 3 decimals).
• Covid-19 Data showed that 22% of people in a small town was infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents was infected.
• Doctors The drug successfully treats 90% of cases. Calculate the probability that he will cure at least 18 patients out of 20?
• Seeds The germination of seeds of a certain species of carrot is 96%. What is the probability that at least 25 seeds out of 30 will germinate?
• Wimbledon finals Serena Williams made a successful first serve 67% 0f the time in a Wimbledon finals match against her sister Venus. If she continues to serve at the same rate the next time they play and serves 6 times in the first game, determine the probability that: 1.
• 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
• Alopecia Medical literature indicates that 45% of men suffer from alopecia. For random sample of 8 men, calculate the probability that: (a) exactly four men suffer from alopecia. (b) at most two men suffer from alopecia.

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Binomial distribution - math problems. Probability - math problems.