Question

**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.

Answer #1

Solution :

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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Central Limit Theorem. If the random variables X1,
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