A population of values has a normal distribution with u = 180.8 and o= 9.4. You intend to draw a random sample of size n = 69. Find the probability that a single randomly selected value is greater than 179. P(X> 179) = Find the probability that a sample of size n = P(M> 179) = 69 is randomly selected with a mean greater than 179. 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 \( \mu = 180.8 \) and \( \sigma = 9.4 \). You intend to draw a random sample of size \( n = 69 \).

Find the probability that a single randomly selected value is greater than 179.  
\( P(X > 179) = \) [             ]

Find the probability that a sample of size \( n = 69 \) is randomly selected with a mean greater than 179.  
\( P(M > 179) = \) [             ]

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 \( \mu = 180.8 \) and \( \sigma = 9.4 \). You intend to draw a random sample of size \( n = 69 \). Find the probability that a single randomly selected value is greater than 179. \( P(X > 179) = \) [             ] Find the probability that a sample of size \( n = 69 \) is randomly selected with a mean greater than 179. \( P(M > 179) = \) [             ] 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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