A population of values has a normal distribution with μ = 78.9 and σ = 13.8. You intend to draw a random sample of size n = 61. Find the probability that a single randomly selected value is between 78.7 and 84.4. P(78.7 < X < 84.4) = Find the probability that a sample of size n = 61 is randomly selected with a mean between 78.7 and 84.4. P(78.7 < M < 84.4) = 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 Adri-N T.
Step 1
For the first question, we have: z1 = (78.7 - 78.9) / 13.8 = -0.0145 z2 = (84.4 - 78.9) / 13.8 = 0.3978 Using a standard normal distribution table or calculator, we can find the probabilities for each z-score: P(z1 < Z < z2) = P(-0.0145 < Z < 0.3978) = 0.3211 Show more…
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