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Suppose that a company is testing a new product and surveys potential consumers. The people who...
USA Today reported that about 20% of all people in the United States are illiterate. Suppose you take seven people at random off a city street. (a) Make a histogram showing the probability distribution of the number of illiterate people out of the seven people in the sample (b) Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.) μ = people σ = people Find the expected number of people in this sample who...
4. A lift has an occupancy warning of no more than 25 people and of total weight no more than 1950kg. For a population of users, suppose weights are normally distributed with mean 75kg and standard deviation 10kg (a) What is the probability that the total weight of a random sample of 25 people from the population exceeds 1950kg? (b) Calculate the probability that a random sample of 24 people sets the alarm off. (c) Suppose people carry things with...
1. The response rate to telephone polls is around 2%. Of people who respond to telephone polls. currently about 40% approve of the President Suppose we perform a telephone poll by calling a random sample of 50,000 registered voters. (a) Let X be a binomial random variable representing the number of people who respond to the telephone poll. What are the expected value and standard deviation of X? (b) Let Y be a binomial random variable representing the number of...
1. Suppose that 81% of the people in Houston live in the city and 19% of the people live in the suburbs. If the 21,000 undergraduate students from UH represent a random sample of the population, what is the probability that the number of UH undergraduates are from suburbs will be fewer than 4,000? (Hint: Apply normal approximation to binomial probability via CLT.) 2. Suppose that the body mass index (BMI) measure for adults is normally distributed with mean 21.7...
4. A lift has an occupancy warning of no more than 25 people and of total weight no more than 1950kg. For a population of users, suppose weights are normally distributed with mean 75kg and standard deviation 10kg. (a) What is the probability that the total weight of a random sample of 25 people from the population exceeds 1950kg? (b) Calculate the probability that a random sample of 24 people sets the alarm off. (c) Suppose people carry things with...
Part 1 Suppose that 2 batteries are randomly chosen without replacement from a group of 12 batteries: 3 new, 4 used (working), and 5 defective. Let the random variable X denote the number of new batteries chosen and the random variable Y denote the number of used batteries chosen. The joint distribution fxy is given in the following table: 0 12 17663/6 120/6612/66 1. Calculate P ( X 1 ,Y > 1) 2. Find the marginal probability mass function fx...
please solve 22.1, using the Theorem given. Thank you. Theorem 22.1. Suppose that n people (n 2 2) are at a party. Then there exist at least two people at the party who know the same number of people present First you need to know the rules. We will assume that no one knows him- or herself. We will also assume that if x claims to know y, then y also knows x. The idea behind the proof is this,...
A sample of 129 potential customers was asked to use your new product and the product of the leading competitor. After one week, they were asked to indicate which product they preferred. Let X = the number of customers who said that they preferred your product. In the sample, X = 44. What is the lower endpoint of a 95% confidence interval for p, the proportion of potential customers who prefer your product to that of your competitor? (Apply the...
2. Suppose a r.v. X has the density function 2 x, for 0<x<1 f(x) = 10, otherwise Observe X independently for three times, let y denote the number of an event {X<0.5) occurring in three times. (1) What is the probability of the event {X<0.5}? (2) What is the probability distribution of Y ? Write out its probability mass function
Problem #1 (10 points) Suppose you must establish regulations concerning the maximum number of people who can occupy an elevator. A study of elevator occupancies indicates that, if eight people occupy the elevator, the probability distribution of the total weight of the eight people has a mean equal to 1,200 pounds and a variance equal to 9,800 lbs2 . Assume that the probability distribution is approximately normal. We are interested in the probabilities of exceeding 1,300 pounds and 1,500 pounds...