A population of values has a normal distribution with μ = 50 and σ = 4.2 . You intend to draw a random sample of size n = 196 . Find the probability that a single randomly selected value is between 49.1 and 50.1. P(49.1 < X < 50.1) Find the probability that a sample of size n = 196 is randomly selected with a mean between 49.1 and 50.1. P(49.1 < M < 50.1) Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Added by Jacqueline B.
Step 1
1 and 50.1. z = (X - μ) / σ For X = 49.1: z1 = (49.1 - 50) / 4.2 ≈ -0.214 For X = 50.1: z2 = (50.1 - 50) / 4.2 ≈ 0.024 Now, we can find the probability that a single randomly selected value is between 49.1 and 50.1 using the standard normal table or a Show more…
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