Show supporting work. Historically 22% of all adults in the state regularly smoked cigars or cigarettes. And a standard deviation A measure of the variability of proportions computed from samples of the same size. Often sampling is done in order to estimate the proportion of a population that has a specific characteristic, such as the proportion of all items coming off an assembly line that are defective or the proportion of all people entering a retail store who make a purchase before leaving. Suppose that 8% of all males suffer some form of color blindness. An airline claims that 72% of all its flights to a certain region arrive on time. After the low-cost clinic had been in operation for three years, that figure had risen to 86%. A state public health department wishes to investigate the effectiveness of a campaign against smoking. He knows that five years ago, 38% of all passenger vehicles in operation were at least ten years old. N is the number of trials. An airline claims that there is a 0.10 probability question. The population proportion is denoted p and the sample proportion is denoted Thus if in reality 43% of people entering a store make a purchase before leaving, p = 0. In an effort to reduce the population of unwanted cats and dogs, a group of veterinarians set up a low-cost spay/neuter clinic.
An airline claims that there is a 0. Suppose that 29% of all residents of a community favor annexation by a nearby municipality. A humane society reports that 19% of all pet dogs were adopted from an animal shelter. Find the probability that in a random sample of 50 motorists, at least 5 will be uninsured. Using the binomial distribution, it is found that there is a: a) 0. An airline claims that there is a 0.10 probability and statistics. An online retailer claims that 90% of all orders are shipped within 12 hours of being received. Find the probability that in a random sample of 600 homes, between 80% and 90% will have a functional smoke detector. Find the probability that in a random sample of 275 such accidents between 15% and 25% involve driver distraction in some form. In actual practice p is not known, hence neither is In that case in order to check that the sample is sufficiently large we substitute the known quantity for p. This means checking that the interval.
The Central Limit Theorem has an analogue for the population proportion To see how, imagine that every element of the population that has the characteristic of interest is labeled with a 1, and that every element that does not is labeled with a 0. An airline claims that there is a 0.10 probability sampling. If Sam receives 18 or more upgrades to first class during the next. An outside financial auditor has observed that about 4% of all documents he examines contain an error of some sort. Viewed as a random variable it will be written It has a mean The number about which proportions computed from samples of the same size center.
You may assume that the normal distribution applies. Clearly the proportion of the population with the special characteristic is the proportion of the numerical population that are ones; in symbols, But of course the sum of all the zeros and ones is simply the number of ones, so the mean μ of the numerical population is. In a random sample of 30 recent arrivals, 19 were on time. In the same way the sample proportion is the same as the sample mean Thus the Central Limit Theorem applies to However, the condition that the sample be large is a little more complicated than just being of size at least 30. Suppose random samples of size n are drawn from a population in which the proportion with a characteristic of interest is p. The mean and standard deviation of the sample proportion satisfy. Sam is a frequent flier who always purchases coach-class.
Lies wholly within the interval This is illustrated in the examples. Suppose this proportion is valid. A consumer group placed 121 orders of different sizes and at different times of day; 102 orders were shipped within 12 hours. An ordinary die is "fair" or "balanced" if each face has an equal chance of landing on top when the die is rolled. 43; if in a sample of 200 people entering the store, 78 make a purchase, The sample proportion is a random variable: it varies from sample to sample in a way that cannot be predicted with certainty. In a survey commissioned by the public health department, 279 of 1, 500 randomly selected adults stated that they smoke regularly. Item a: He takes 4 flights, hence. Binomial probability distribution.
90,, and n = 121, hence. At the inception of the clinic a survey of pet owners indicated that 78% of all pet dogs and cats in the community were spayed or neutered. Be upgraded 3 times or fewer? He commissions a study in which 325 automobiles are randomly sampled. Thus the population proportion p is the same as the mean μ of the corresponding population of zeros and ones.
B. Sam will make 4 flights in the next two weeks. Item b: 20 flights, hence. 38 means to be between and Thus. 6 Distribution of Sample Proportions for p = 0. Would you be surprised. Which lies wholly within the interval, so it is safe to assume that is approximately normally distributed. Here are formulas for their values. For each flight, there are only two possible outcomes, either he receives an upgrade, or he dos not. In each case decide whether or not the sample size is large enough to assume that the sample proportion is normally distributed. Assuming the truth of this assertion, find the probability that in a random sample of 80 pet dogs, between 15% and 20% were adopted from a shelter. 1 a sample of size 15 is too small but a sample of size 100 is acceptable. 39% probability he will receive at least one upgrade during the next two weeks. 71% probability that in a set of 20 flights, Sam will be upgraded 3 times or fewer. D. Sam will take 104 flights next year.
First verify that the sample is sufficiently large to use the normal distribution. The probability of receiving an upgrade in a flight is independent of any other flight, hence, the binomial distribution is used to solve this question. A random sample of size 1, 100 is taken from a population in which the proportion with the characteristic of interest is p = 0. Assuming this proportion to be accurate, find the probability that a random sample of 700 documents will contain at least 30 with some sort of error.
Of them, 132 are ten years old or older. Suppose that in 20% of all traffic accidents involving an injury, driver distraction in some form (for example, changing a radio station or texting) is a factor. This outcome is independent from flight. 38, hence First we use the formulas to compute the mean and standard deviation of: Then so. P is the probability of a success on a single trial. Suppose that in a population of voters in a certain region 38% are in favor of particular bond issue. C. What is the probability that in a set of 20 flights, Sam will. In one study it was found that 86% of all homes have a functional smoke detector. Find the probability that in a random sample of 450 households, between 25 and 35 will have no home telephone.
The parameters are: - x is the number of successes. To be within 5 percentage points of the true population proportion 0.
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