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
Algebra.Com
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.
RELATED QUESTIONS
A population of values has a normal distribution with
μ
=
117.7
μ=117.7
and
σ
(answered by ikleyn)
A population of values has a normal distribution with μ=17.9 and σ=94.8. You... (answered by Edwin McCravy)
A population of values has a normal distribution with μ =226.1 and σ =41.6
You intend... (answered by Boreal)
A population of values has a normal distribution with
μ = 12.1 and σ = 67.9. You... (answered by robertb)
A population of values has a normal distribution with
u = 86.4 and σ = 83.3. You... (answered by robertb)
A population of values has a normal distribution with mean = 173 and standard deviation = (answered by Theo)
A population of values has a normal distribution with μ=225.8 and σ=87.4. You... (answered by Theo)
A population of values has a normal distribution with μ=206.3 and σ=51.5. You... (answered by Boreal)
A population of values has an unknown distribution with
μ=250 and σ=7.9. You intend (answered by Boreal)