4. A company finds that 18% of all new employees resign during the first year. 16 new employees are selected at random. Find the following probabilities. a. In the binomial experiment, describe the two outcomes associated with the random variable. 1. _________________ 2. _________________ b. P (exactly half resign in the first year) _________________ c. P (none of them resign in the first year) _________________ d. P (at most 4 resign in the first year) _________________ e. P (at least 6 resign in the first year) _________________ 5. In a clinical trial of a new allergy medicine, researchers found that 3 out of every 5 allergy sufferers complain of drowsiness when using the drug. a. State the value of p. _________________ b. In a group of 850 allergy sufferers who used this medicine, how many would you expect on average to experience drowsiness from the medicine? _________________ c. In a group of 850 allergy sufferers who used this medicine, find the probability that more than 550 of them complained of drowsiness? __________________ Answer the following questions. Put the answers on the blanks! Use 2 decimal places for z-scores and 4 decimal places for probabilities. 6. A statistics professor plans her tests so carefully that the lengths of time for her students to take the tests are uniformly distributed between 50 and 75 minutes. a. Draw a graph of the uniform density function (include the height!). If a student is randomly selected, find (Show your work) b. P (the time it takes the student to take the test is between 55 and 60 minutes) _______________________ c. P (the time it takes the student to take the test is between 73 and 75 minutes) _______________________