A population of values has a normal distribution with μ = 145.1 and σ = 60.3. You intend to draw a random sample of size n = 128. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is between 129.6 and 139.2. P(129.6 X 139.2) = Find the probability that a sample of size n = 128 is randomly selected with a mean between 129.6 and 139.2. P(129.6139.2) =

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Question 3
145.1 and o= 60.3. You intend to draw a
A population of values has a normal distribution with μ =
random sample of size n = 128. Please show your answers as numbers accurate to 4 decimal places.
Find the probability that a single randomly selected value is between 129.6 and 139.2.
P(129.6 < X < 139.2) =
Find the probability that a sample of size n = 128 is randomly selected with a mean between 129.6 and
139.2.
P(129.6 139.2) =
<
Transcribed Image Text:Question 3 145.1 and o= 60.3. You intend to draw a A population of values has a normal distribution with μ = random sample of size n = 128. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is between 129.6 and 139.2. P(129.6 < X < 139.2) = Find the probability that a sample of size n = 128 is randomly selected with a mean between 129.6 and 139.2. P(129.6 139.2) = <
Question 2
>
A population of values has an unknown distribution with μ = 6.3 and σ = 83.3. You intend to draw a
random sample of size n = 55.
What is the mean of the distribution of sample means?
fã =
(Please enter an exact answer.)
What is the standard deviation of the distribution of sample means?
σx
(Please report your answer accurate to 2 decimal places.)
Transcribed Image Text:Question 2 > A population of values has an unknown distribution with μ = 6.3 and σ = 83.3. You intend to draw a random sample of size n = 55. What is the mean of the distribution of sample means? fã = (Please enter an exact answer.) What is the standard deviation of the distribution of sample means? σx (Please report your answer accurate to 2 decimal places.)
Expert Solution
Step 1

Question.2:-

according to central limit theorem if sample size is large enough i.e. greater than 30 then sampling distribution of mean is approximately normally distributed with mean equal to population mean μ and standard error  σ /√n.

So

Mean = μx  = 6.3 

Standard deviation= 83.3/√55

11.2322

On rounding11.23

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