A population of values has a normal distribution with \mu =49.7 and \sigma =71.9 . You intend to draw a random sample of size n=17 . Find the probability that a single randomly selected value is greater than 11.3. P(X > 11.3) = ? Find the probability that a sample of size n=17 is randomly selected with a mean greater than 11.3. P(M > 11.3) = ? 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 Mallory H.
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3. To find the probability \( P(X > 11.3) \), we need to calculate the z-score for \( X = 11.3 \) using the formula: \[ z = \frac{X - \mu}{\sigma} = \frac{11.3 - 49.7}{71.9} \] Calculate the z-score: \[ z = \frac{-38.4}{71.9} \approx -0.5341 \] Now, use the Show more…
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