For problems 1, 2, and 3, suppose that the normally distributed random variable X has mean and standard deviation . 1. Calculate the z-score of the value x=17. a. 1.67 b. -1.67 c. -5 d. 5 2. Calculate the x-value that corresponds to a z-score of . a. 26.2 b. 17 c. 29 d. 25 3. Find the probability that the variable takes on a value greater than 20. a. 0.5 b. 0.75 c. 0.7 d. 0.25 4. For a normally distributed variable x with mean 12 and standard deviation 4, find the probability that x is between 10 and 15. a. 0.54 b. 0.4 c. 0.8 d. 0.46 5. For a normally distributed variable with mean 51 and standard deviation 6, find the 80th percentile. a. 44 b. 56 c. 54 d. 80
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To calculate the z-score, we use the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation. In this case, x = 17, μ = 1, and σ = 1. So, z = (17 - 1) / 1 = 16. Answer 1: $\boxed{16}$ Show more…
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