Question

A population of values has a normal distribution with μ=200.5μ=200.5 and σ=56.9σ=56.9. You intend to draw a random sample of size n=131n=131.

Find the probability that a single randomly selected value is less than 204.8.
P(X < 204.8) =

Find the probability that a sample of size n=131n=131 is randomly selected with a mean less than 204.8.
P({¯x{x¯ < 204.8) =

Enter your answers as numbers accurate to 4 decimal places. Answers should be obtained using zz scores correct to two decimal places.

Answer 1

Solution:

Given that μ=200.5 and σ = 56.9 we have:
P(X < 204.8) = P(Z < 204.8-200.5/56.9)
= P(Z < 0.08)
= 0.5319
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Now for sample of size n = 131, we need to find
P(X < 204.8) = P[Z < (204.8-200.5)/(56.9/√131)]
= P(Z < 0.8649)
= 0.8051