Apply the Central Limit Theorem for Sample Means
A population of values has a normal distribution with μ=77 and
σ=9.2. You intend to draw a random sample of size n=30.
Find the probability that a sample of size n=30n=30 is randomly selected with a mean less than 76.8.
P(M < 76.8) =
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.
Given that ,
mean = = 77
standard deviation = = 9.2
n = 30
M = = 77 and
M = / n = 9.2 / 30 = 1.6797
P(M < 76.8) = P((M - M ) / M < (76.8 - 77) / 1.6797)
= P(z < -0.119) Using standard normal table.
Probability = 0.4526
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