According to a​ report, 61.3​% of murders are committed with a firearm. ​(a) If 400 murders are randomly​ selected, how many would we expect to be committed with a​ firearm? ​(b) Would it be unusual to observe 254 murders by firearm in a random sample of 400 ​murders? Why?

According to a report, 71.9% of murders are committed with a firearm. (a) If 400 murders are randomly selected, how many would we expect to be committed with a firearm? (b) Would it be unusual to observe 312 murders by firearm in a random sample of 400 murders? Why? (a) We would expect to be committed with a firearm. (b) Choose the correct answer below. A. Yes, because 312 is greater than u + 20. B. No, because 312 is between u - 20 and H+ 20. O C. No, because 312 is greater than p + 2o. D. No, because 312 is less than u - 20. E. Yes, because 312 is between u - 20 and u + 20.

In a memory test, the test subjects are given a large number and are asked to memorize it. Historical records show that 80% of test subjects pass the test. To pass the test, a subject must exactly repeat all the digits in the number after two hours. A random sample of 625 people to take the memory test is going to be chosen. Let p be the proportion of people in the sample who pass the test. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of P. 0 (b) Find the standard deviation of p. 0 (c) Compute an approximation for P(P >0.84), which is the probability that more than 84% of the people in the sample pass the test. Round your answer to four decimal places. 0 X

Are birthdays "evenly distributed" throughout the year, or are they more common during some parts of the year than others? Owners of a children's toy store chain in the Northwest asked just this question. Some data collected by the chain are summarized in the table below. The data were obtained from a random sample of 190 people. The birthdate of each person was recorded, and each of these dates was placed into one of four categories: winter (December 21-March 20), spring (March 21-June 20), summer (June 21-September 20), and fall (September 21-December 20). The numbers in the first row of the table are the frequencies observed in the sample for these season categories. The numbers in the second row are the expected frequencies under the assumption that birthdays are equally likely during each season of the year. The bottom row of numbers gives the following value for each of the season categories. Answer the following to summarize the test of the hypothesis that birthdays are equally…