4. A drug manufacturer claims that its flu vaccine is 85% effective; in other words, each person who is vaccinated stands an 85% chance of developing immunity. Suppose that 200 people
are vaccinated. Let x be the number that develops immunity.
a. What is the distribution of x?

b. What is the mean and standard deviation for x?

c. What is the probability that between 165 and 180 of the 200 people who were vaccinated
develop immunity? (Hint: Use a normal distribution to approximate the distribution of x.)

Questions 9-10. use the table of educational expenditures to answer the questions. k-12 education expenditures population indiana $9.97 billion 6.6 million illinois $28.54 billion 12.9 million kentucky $6.58 billion 4.4 million michigan $16.85 billion 9.9 million ohio $20.23 billion 11.6million 9. if the amount of k-12 education expenses in indiana were proportional to those in ohio, what would have been the expected value of k-12 expenditures in indiana? (give the answer in billions rounded to the nearest hundredth) 10. use the value of k-12 education expenditures in michigan as a proportion of the population in michigan to estimate what the value of k-12 education expenses would be in illinois. a) find the expected value of k-12 expenditures in illinois if illinois were proportional to michigan. (give the answer in billions rounded to the nearest hundredth) b) how does this compare to the actual value for k-12 expenditures in illinois? (lower, higher, same? )

Given the diagram below, michael writes, "segment ac is congruent to segment ac." which of the following reasons allow him to write this statement?

‼️‼️‼️‼️‼️the pressure exerted on the walls of a container by a gas enclosed within it is directly proportional to the temperature of the gas. if the pressure is 6 pounds per square inch when the temperature is 440 f, find the pressure exerted when the temperature of the gas is 380°f. (show work)