Suppose the probability of getting an "A" in a certain class is 0.22. A group of 5 friends is taking the class together. Determine the probability that none of the friends earn an "A" in the class. (Assume that each person's grade is independent of the others.) Describe the design of a simulation to estimate this probability. Explain clearly how you will use the partial table of random digits below to carry out your simulation (attached below). You must perform a minimum of 10 repetitions.

Night Owls proportion of MSU students who regularly sleep less than 8 hours each night is less than the value reported by the MSU psychologist. She randomly selects 215 students and asks them, "Do you regularly sleep less than 8 hours each night?" She finds that 77 of the 215 students answered "yes" to the question. A MSU psychologist reports that 40% of MSU students regularly sleep less than 8 hours each night. Cindy believes that the actual 1. Which one of the following statements about the number 40% is correct? A. It is a sample statistic. B. It is a standard error. C. It is a margin of error. D. It is a claimed parameter. 2. Choose the null and alternative hypotheses Cindy should use to test her theory. А. Но : р %3D 0.4, Нд : р+0.4 В. Но : р %3D 0.4, На : р 0.4 3. If you assume that the observations in the sample are independent, what is the smallest value the sample size could be to meet the conditions for this hypothesis test? OA. 28 В. 10 C. None of the above D. 20 Е. 77 OF.…

For two events A and B, P(A) = 0.55, P(B) = 0.40, and P(A & B) = 0.22. Find P(A|B). Express your answer as a decimal rounded to 2 digits, eg. 0.96.

Yearly, students are invited to membership in the honor society for your major if their class rank is at least in the 90th percentile for all students in that major. In 2019 you ranked 30 out of 128 students in your major. Will you be invited to membership?