SOLUTION: A population of values has a normal distribution with μ=13.7 and σ=81.6.If a random sample of size n=20 is selected
Find the probability that a single randomly selected value
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Find the probability that a single randomly selected value
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Question 1197074: A population of values has a normal distribution with μ=13.7 and σ=81.6.If a random sample of size n=20 is selected
Find the probability that a single randomly selected value is less than -8.2. Round your answer to four decimals
P(X < -8.2)=
Find the probability that a sample of size .n=20 is randomly selected with a mean less than -8.2. Round your answer to four decimals.
P(M < -8.2) = Found 2 solutions by Theo, math_tutor2020:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! when you are dealing with a sample of one element, you use the standard deviation.
when you are dealing with a the mean of a sample containing numerous elements, you use the standard error.
standard error is equal to standard deviation / square root of sample size.
A population of values has a normal distribution with μ=13.7 and σ=81.6.If a random sample of size n=20 is selected
Find the probability that a single randomly selected value is less than -8.2. Round your answer to four decimals.
z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard deviation.
formula becomes:
z = (-8.2 - 13.7) / 81.6 = -21.9 / 81.6 = -.2683823529
P(z < -.2683823529) = .3942 rounded to 4 decimal places.
that's the same as p(x < -8.2)
Find the probability that a sample of size n=20 is randomly selected with a mean less than -8.2. Round your answer to four decimals.
z = (x - m) / s
z is the z-score
x is the raw score
m is the mean
s is the standard error = 81.6 / sqrt(20) = 18.2463147
formula becomes:
z = (-8.2 - 13.7) / 18.2463147 = -21.9 / 18.2463147 = -1.20024237
P(z < -1.20024237) = .1150 rounded to 4 decimal places.
that's the same as p(x < -8.2)
when using the calculator, SD = standard deviation when dealing with a sample of 1 element, and SD = standard error when dealing with the mean of a sample with multiple elements.
if you give the mean as 0 and SD = 1, you are looking for the probability of being less than the z-score.
if you give the mean as what it is and SD as either the standard deviation or the standard error, you are looking for the probability of being less than the raw score.
let me know if you have any further questions regarding this.
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