7. Suppose that ladybugs are distributed randomly and uniformly on the leaves of apple trees at a rate of à per tree. In an orchard of 100 trees, 58 contained no ladybugs, and 42 contained one or more ladybugs. What is the maximum likelihood estimate of 1? Hints: There are two different distributions involved in this question, and you will need to use the Invariance Property. A) 0.42 B) 0.58 C) 0.545 D) 4.060

The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences. This problem is an example of a Teens Adults Coffee 50 200 E!! Tea 100 150 Soft 200 200 Drink Other 50 50 Select one: O a. normally distributed variable O b. test for independence O c. binomial distributed variable O d. multinomial population

Normal Distribution Problem: A certain component for the newly developed electronic diesel engine is considered to be defective if its diameter is less than 8 mm or greater than 10.5 mm. The distributions of the diameters of these parts is known to be normal with a mean of 9.0 mm and a standard deviation of 1.5 mm. If a component is randomly selected, what is the probability that it will be defective? Q: Do I add the Right and Left tails and that's my total probability of defectiveness? Or, Do I take the Normal.Dist (from Excel) to the left of 10.5 minus the N.D left of 8 for a total of .588852 probability that it will be defective (that's a lot)? Please help! And, thank you in advance!

3a) The mean IQ of 200 patients in a psychiatric hospital is 91, with a variance of 16, and the distribution is highly negatively skewed. Between what two IQ scores would we expect to find at least 160 of the patients falling? b) If the distribution was mound-shaped and symmetrical, with the same mean and standard deviation as in part A, approximately how many patients would have IQ scores at or below the 5th percentile or above a score of 97? Answers: a) 82 to 100 b) 28.5 or 29