Math 1401 Quiz 8 PDF

# Quiz 8 ## Name: SOLUTION ## Score: /25 ## Math 1401 ### 1. The graph below shows the graphs of several normal distributions, labeled A, B, C, on the same axis. * (a) (5 points) Rank the three normal distributions according to their means. * Least mean: **B** * Middle mean: **C** *...

# Quiz 8 ## Name: SOLUTION ## Score: /25 ## Math 1401 ### 1. The graph below shows the graphs of several normal distributions, labeled A, B, C, on the same axis. * (a) (5 points) Rank the three normal distributions according to their means. * Least mean: **B** * Middle mean: **C** * Greatest mean: **A** * (b) (5 points) Rank the three normal distributions according to their standard deviations. * Least standard deviation: **C** * Middle standard deviation: **A** * Greatest standard deviation: **B** ### 2. Suppose that the times to complete a particular obstacle course are normally distributed, with mean 89 seconds and standard deviation 14 seconds. * (a) (3 points) Compute the z-score corresponding to time 54 seconds. $z = \frac{54 - 89}{14} = -2.5$ * (b) (4 points) Use your above answer to determine the probability that a randomly selected finishing time is under 54 seconds. * table: .0062 ### 3. Suppose that you roll a 6-sided die 400 times, and we wish to compute the probability of the die landing on an odd number at least 220 times. This is a binomial distribution problem, but it is unrealistic to compute this probability exactly, so will approximate the binomial distribution with the normal distribution. * (a) (4 points) Here we roll the die 400 times and let X be the number of times the die lands on an odd number. We are approximating the binomial distribution X ~ B(n, p) with a normal distribution N(μ, σ). Determine the appropriate values of n, p, μ, σ. * n = 400 * p = 1/2 * μ = np = 400(1/2) = 200 * σ = √np(1-p) = √400(1/2)(1/2) = √100 = 10 * (b) (4 points) Now using your normal distribution N(μ, σ) from part (a), estimate the probability of the die landing on an odd number at least 220 times. Show work. * using N(200, 10) * P(X ≥ 219.5) ~ .0256 * z = (219.5 - 200) / 10 = -1.95, table: .9744 ---- * This quiz continues on back.