STAT 235 - BSJUUFO )PNFXPSL 3 l. The time takes for a symphony orchestra to play Beethoven's Ninth Symphony has a normal distribution with a mean of 64.3 minutes and a standard deviation of I .15 minutes. If an orchestra plays it so slowly, that 80% of the other orchestras play faster than the orchestra, how long does the orchestra play? 2. State whether or not the normal approximation to the binomial is appropriate in each of the following situa- tions. (a) n=500, p=0.33, (b) n=400, p=0.01, (c) n=100, p=0.61. 3. Suppose in UMKC 30% of the students live in apartments, and 200 students are randomly selected. Let X I be the number of students living in apartments out of those 200 students. (a) Is X a binomial random variable? Justify. If yes, identify n and p. (b) Compute the mean and standard deviation of X. (c) Are the conditions ofNormal approximation to the binomial satised for this study? (d) What is the normal distribution by which X is approximated? (e) Approximately what is the probability that the number of students living in apartments out of those 200 students will be between 50 and 75 inclusive. 4. A population has a distribution that is skewed to the left. Indicate in which of the following cases the central limit theorem will apply to describe the sampling distribution of the sample mean. a.n=400 b.n=25 c.n=36