A population of values has a normal distribution with u = 20.3 and o = 86.5. You intend to draw a random sample of size n = 205. Find the probability that a single randomly selected value is greater than 29.4. P(X > 29.4) = Find the probability that a sample of size n = 205 is randomly selected with a mean greater than 29.4. P(M > 29.4) = 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.

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A population of values has a normal distribution with \( \mu = 20.3 \) and \( \sigma = 86.5 \). You intend to draw a random sample of size \( n = 205 \).

Find the probability that a single randomly selected value is greater than 29.4.

\[ P(X > 29.4) = \, \]

Find the probability that a sample of size \( n = 205 \) is randomly selected with a mean greater than 29.4.

\[ P(M > 29.4) = \, \]

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.
Transcribed Image Text:A population of values has a normal distribution with \( \mu = 20.3 \) and \( \sigma = 86.5 \). You intend to draw a random sample of size \( n = 205 \). Find the probability that a single randomly selected value is greater than 29.4. \[ P(X > 29.4) = \, \] Find the probability that a sample of size \( n = 205 \) is randomly selected with a mean greater than 29.4. \[ P(M > 29.4) = \, \] 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.
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