A population of values has a normal distribution with
μ=148.3μ=148.3 and σ=92.3σ=92.3. You intend to draw a random sample
of size n=49n=49.
Find the probability that a single randomly selected value is less
than 144.3.
P(X < 144.3) =
Find the probability that a sample of size n=49n=49 is randomly
selected with a mean less than 144.3.
P(M < 144.3) =
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.
Let X ~ Normal ( )
n = sample size = 49
1) P( X < 144.3)
Let's find Z score as
So P( X < 144.3)) = P( Z < -0.04334 ) = "=NORMSDIST(-0.04334)"= 0.4827
P( M < 144.3)
Z score formula for sample mean and given value of n is as follow:
So P( M < 144.3)) = P( Z < -0.30336 ) = "=NORMSDIST(-0.30336)" = 0.3808
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