SOLUTION: A population of values has a normal distribution with μ=245.9 and σ=99.9. You intend to draw a random sample of size n=157. Find the probability that a single randomly selecte

Question 1147716: A population of values has a normal distribution with μ=245.9 and σ=99.9. You intend to draw a random sample of size n=157.
Find the probability that a single randomly selected value is less than 260.3.
P(X < 260.3) =
Find the probability that a sample of size n=157 is randomly selected with a mean less than 260.3.
P(M < 260.3) =
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.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
(1) z-score = (260.3 - 245.9)/99.9 is approximately 0.144
:
Probability (P) (X < 260.3) = 0.557
:
(2) square root(157) = 12.53
:
standard error = 99.9/12.53 = 7.973
:
z-score = (260.3 - 245.9)/7.973 = 1.806
:
P (M < 260.3) = 0.965
:

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