SOLUTION: A population of values has a normal distribution with μ=149.1 and σ=24.You intend to draw a random sample of size n=67 . Find the probability that a single randomly selected v

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Question 1165347: A population of values has a normal distribution with μ=149.1 and σ=24.You intend to draw a random sample of size n=67 .
Find the probability that a single randomly selected value is greater than 143.8.
P(X > 143.8) =

Find the probability that a sample of size n=67 is randomly selected with a mean greater than 143.8.
P(M > 143.8) =

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 by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
z=(x-mean)/sd
z > (143.8-149.1)/24 or greater than -0.2208. That probability is 0.5874
for a sample of 67, the SEM is 24/sqrt(67). That is the sd of the distribution of sample means with n=67
that SEM is 2.93
z > -1.808 That probability is 0.9647
The distribution of the sample means for a given size sample is narrower than the distribution for a single selection. The greater the sample, the narrower the distribution.