IV. V. The management of a company ordered a study to determine the distribution of hamburgers purchased by the company that could be contaminated with Salmonella in a lot of them. According to the study, 25% of the hamburgers were contaminated. If a random sample of 10 hamburgers is chosen to be tested. a) What is the probability that three hamburgers are contaminated? Remember what to calculate in this case is P(k=3) b) What is the probability that at least 2 are contaminated? Remember what to calculate in this case is P(ksZ) c) Calculate the expected value (mean) d) The standard deviation An insurance agent sells policies to ve people of the same age and in good health. According to current tables, the probability that a person in these conditions will live 30 years or more is 2l3. Find the probability that, after 30 years, there will be: a. Exactly two people b. At least three people Given the normal distribution nd the area under the curve that falls a. To the left of z=0.85 b. To the right of z=-0.95 c. Between z=-2 and z=2 Given the standard normal distribution, find the value of k such that a. P(Zk) =0.9 Given a sampling distribution with p =20 and 0:5 a. The area of the normal curve to the right of x=25 b. The value of x that contains 80% of the area of the normal curve on the left. c. the values of x that contain 90% of the area closest to the mean VI. VII. VIII. IX. XI. In a city it is estimated that the maximum temperature in June follows a normal distribution, with a mean of 23 and a standard deviation of 3. Calculate the number of days of the month in which it is expected to reach maximums between 21 and 27". It is assumed that the results of an exam follow a normal distribution with a mean of 78 and a standard deviation of 36. What is the probability that a person who takes the exam obtains a grade greater than 72? Several intelligence tests gave a score that follows a normal law with mean 100 and standard deviation 15 a. Determine the percentage of the population that would obtain a coefcient between 95 and 110 b. What interval centered at 100 contains 50% of the population? c. In a population of 2500 individuals, how many individuals are expected to have a coefcient greater than 125? A manufacturer of electric lamps is testing a new production method that will be considered acceptable if the lamps produced by this method give rise to a normal population of mean life of 2400 hours, with a standard deviation equal to 300. A sample is taken of 100 lamps produced by this method and this sample will have an average duration of 2320 hours. Can the validity hypothesis of the new manufacturing process be accepted with a risk equal to or less than 5%? In a hospital, the temperature of a sample of 64 patients has been taken to estimate the average temperature of their patients. The sample mean has been 37.100, and the standard deviation for the entire population is known to be 1.0400. Obtain a 90% condence interval for the population mean. You want to start an investigation to estimate the average time that projects developed by Enigma Project S.A. take. The estimate must be made at a confidence level of 90% and a maximum permissible error of 15 days. Assuming that the standard deviation of project completion times is 80 days, how many of the company's completed projects should constitute the sample