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Suppose that one requirement is that at most 4% of all packages marked 500 grams can weigh less than 490 grams. Samples of size n produced sample proportions as shown. In a survey commissioned by the public health department, 279 of 1, 500 randomly selected adults stated that they smoke regularly. 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. An outside financial auditor has observed that about 4% of all documents he examines contain an error of some sort. An airline claims that there is a 0. An airline claims that there is a 0.10 probability distribution. Using the value of from part (a) and the computation in part (b), The proportion of a population with a characteristic of interest is p = 0. The proportion of a population with a characteristic of interest is p = 0. A random sample of size 1, 100 is taken from a population in which the proportion with the characteristic of interest is p = 0. The probability is: In which: Then: 0. 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. Find the probability that in a random sample of 450 households, between 25 and 35 will have no home telephone.
In an effort to reduce the population of unwanted cats and dogs, a group of veterinarians set up a low-cost spay/neuter clinic. Because it is appropriate to use the normal distribution to compute probabilities related to the sample proportion. An airline claims that there is a 0.10 probability density. 39% probability he will receive at least one upgrade during the next two weeks. Historically 22% of all adults in the state regularly smoked cigars or cigarettes. 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. This gives a numerical population consisting entirely of zeros and ones.
A consumer group placed 121 orders of different sizes and at different times of day; 102 orders were shipped within 12 hours. Suppose that 29% of all residents of a community favor annexation by a nearby municipality. Find the probability that in a random sample of 50 motorists, at least 5 will be uninsured. An airline claims that there is a 0.10 probability theory. For large samples, the sample proportion is approximately normally distributed, with mean and standard deviation. This outcome is independent from flight.
Suppose 7% of all households have no home telephone but depend completely on cell phones. Item a: He takes 4 flights, hence. 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. 90,, and n = 121, hence. For each flight, there are only two possible outcomes, either he receives an upgrade, or he dos not. If Sam receives 18 or more upgrades to first class during the next. Find the probability that in a random sample of 275 such accidents between 15% and 25% involve driver distraction in some form. Sam is a frequent flier who always purchases coach-class. Nine hundred randomly selected voters are asked if they favor the bond issue.
First class on any flight. Would you be surprised. He knows that five years ago, 38% of all passenger vehicles in operation were at least ten years old. In a random sample of 30 recent arrivals, 19 were on time. Be upgraded 3 times or fewer? A humane society reports that 19% of all pet dogs were adopted from an animal shelter. The sample proportion is the number x of orders that are shipped within 12 hours divided by the number n of orders in the sample: Since p = 0. Find the probability that in a random sample of 250 men at least 10% will suffer some form of color blindness. 38, hence First we use the formulas to compute the mean and standard deviation of: Then so.