Binomials - Speech or Presentation Example

PART A The probability distribution of a random variable X is given. x 2 3 4 P(X = x) 0.2 0.4 0.3 0 Compute the mean, variance, andstandard deviation of X. (Round your answers to two decimal places.) mean 2.3variance 0.81standard deviation 0.92. The probability distribution of a random variable X is given. x -2 -1 0 1 2 P(X = x) 1/16 4/16 6/16 4/16 1/16 Compute the mean, variance, and standard deviation of X. mean 0variance 1standard deviation 13. The probability distribution of a random variable X is given.

x 450 460 540 555 570 P(X = x) 0.2 0.1 0.4 0.2 0.1 Compute the mean, variance, and standard deviation of X. (Round your answers to two decimal places.) mean 520variance 1995standard deviation 44.674. Find the variance of the probability distribution for the histogram shown. (Round your answer to two decimal places.) no histogram displayed5. Rosa Walters is considering investing $10,000 in two mutual funds. The anticipated returns from price appreciation and dividends (in hundreds of dollars) are described by the following probability distributions.

Mutual Fund A Returns Probability -2 0.4 8 0.3 10 0.3 Mutual Fund B Returns Probability -4 0.4 7 0.3 8 0.3 (a) Compute the mean and variance for Mutual Fund A. mean 6.4dollars variance 6.64dollars2 Compute the mean and variance for Mutual Fund B. mean 2.9dollars variance 31.89dollars2 (b) Which investment would provide Rosa with the highest expected return (the greater mean)? Mutual Fund B(c) In which investment would the element of risk be less (that is, which probability distribution has the smaller variance)?

Mutual Fund A 6. The following table gives the total caseload (in millions) in a states courts from 2004 through 2009. Year 2004 2005 2006 2007 2008 2009 Cases 4.9 4.3 4.6 4.2 4.8 4.2 Find the mean of the total caseload for the states courts from 2004 through 2009. (Round your answer to two decimal places.)4.5million casesWhat is the standard deviation for these data? (Round your answer to two decimal places.)10.0.9million cases 7. Suppose X is a random variable with mean μ and standard deviation σ.

If a large number of trials is observed, at least what percentage of these values is expected to lie between μ - 4σ and μ + 4σ? (Round your answer to the nearest whole number.)at least 67% 8. A Christmas tree light has an expected life of 180 hr and a standard deviation of 2 hr. (a) Find a bound on the probability that one of these Christmas tree lights will require replacement between 170 hr and 190 hr. (Enter your answer to two decimal places.)at least 0.6(b) Suppose a large city uses 190,000 of these Christmas tree lights as part of its Christmas decorations.

Estimate the number of lights that are likely to require replacement between 160 hr and 200 hr of use.76000lights.9. Find C(n, x)pxqn - x for the given values of n, x, and p. (Round your answer to four decimal places.) n = 7, x = 2, p = 13 ( fraction 1/3 )0.3110. Find C(n, x)pxqn - x for the given values of n, x, and p. (Round your answer to four decimal places.) n = 7, x = 3, p = 0.3 =0.1611. Use the formula C(n, x)pxqn - x to determine the probability of the given event. (Round your answer to four decimal places.) The probability of exactly no successes in seven trials of a binomial experiment in which p = 13 ( fraction 1/3 ) 0.007812. Use the formula C(n, x)pxqn - x to determine the probability of the given event.

(Round your answer to four decimal places.) The probability of at least five successes in ten trials of a binomial experiment in which p = 12 (fraction ½ )=0.2513. A fair die is rolled four times. Calculate the probability of obtaining exactly two 6s. (Round your answer to four decimal places.)0.001514. Let X be the number of successes in five independent trials of a binomial experiment in which the probability of success is . ( fraction 4/5)p = 45. Find the following probabilities. (Round your answers to four decimal places.) (a) m0.00067(b) P(2 = X = 4)0.007215. Let the random variable X denote the number of girls in a five-child family.

If the probability of a female birth is 0.5, find the following probabilities. (a) Find the probability of 0, 1, 2, 3, 4, and 5 girls in a five-child family. (Round your answers to three decimal places.) P(0 girls) = 0.031P(1 girl) = 0.156P(2 girls) = 0.124P(3 girls) = 0.124P(4 girls) = 0.156P(5 girls) = 0.031(b) Construct the binomial distribution, and draw the histogram associated with this experiment. (c) Compute the mean and the standard deviation of the random variable X. (Round your standard deviation to three decimal places.)mean 2.5girls s.d =2.2girls16.

Suppose 30% of the restaurants in a certain part of a town are in violation of the health code. A health inspector randomly selects six of the restaurants for inspection. (Round your answers to four decimal places.) (a) What is the probability that none of the restaurants are in violation of the health code?0.11(b) What is the probability that one of the restaurants is in violation of the health code?0.16(c) What is the probability that at least two of the restaurants are in violation of the health code?0.4717.

A new drug has been found to be effective in treating 70% of the people afflicted by a certain disease. If the drug is administered to 600 people who have this disease, what are the mean and the standard deviation of the number of people for whom the drug can be expected to be effective? (Round your standard deviation to two decimal places.) mean 420people standard deviation 274.95people PART B--will be on another word doc