Question
In: Statistics and Probability
You have a normal population of scores with μ = 50 and σ = 14. We...
You have a normal population of scores with μ = 50 and σ = 14. We obtain a random sample of n = 36. What is the probability that the sample mean will be less than 54?
Solutions
Expert Solution
Here we need to find 
As population is normal, as per central limit sample mean is also normally distributed so we can convert sample mean to z
orchestra answered 1 year agoRelated Solutions
We have two normal populations with unknown means μ₁ and μ₂ and a common variance σ²....
We have two normal populations with unknown means μ₁ and μ₂ and
a common variance σ². Two independent samples are randomly drawn
from the populations with the following data: n₁ = 26
xത₁ = 8.35 s₁ = 1.7 n₂ = 34 xത₂ = 7.46 s₂ = 2.2
(a)[5] At the level of significance α = 0.01, test H₀: μ₁ = μ₂
versus H₁: μ₁ ≠ μ₂. Sketch the test.
(b)[2] Sketch and find the p‐value of the test in part...
We have two normal populations with unknown means μ₁ and μ₂ and a common variance σ²....
We have two normal populations with unknown means μ₁ and μ₂ and
a common variance σ². Two independent samples are randomly drawn
from the populations with the following data:
n₁ = 26 xത₁ = 8.35 s₁ = 1.7
n₂ = 34 xത₂ = 7.46 s₂ = 2.2
(a)[5] At the level of significance α = 0.01, test H₀: μ₁ = μ₂
versus H₁: μ₁ ≠ μ₂. Sketch the test.
(b)[2] Sketch and find the p‐value of the test in part...
A population of scores with a μ = 43 a n d σ = 8 is...
A population of scores with a μ = 43 a n d σ = 8 is standardized
to create a new population distribution with a μ = 50 a n d σ = 10
. What is the new X value for each of the following scores from the
original population?
a. X = 43
b. X = 47
c. X = 55
d. X = 35
We have a normal population of scores, with ? = 55 and ? = 17. If...
We have a normal population of scores, with ? = 55 and ? = 17.
If we select a random sample of 100 participants and obtain a mean
of 57, is that a typical mean value for this distribution based on
the values that cutoff the middle 95%?
We have a normal probability distribution for variable x with μ = 24.8 and σ =...
We have a normal probability distribution for variable x with μ
= 24.8 and σ = 3.7. For each of the following, make a pencil sketch
of the distribution & your finding. Using 5 decimals, find:
(a)[1] PDF(x = 30); [use NORM.DIST(•,•,•,0)]
(b)[1] P(x ≤ 27); [use NORM.DIST(•,•,•,1)]
(c)[1] P(x ≥ 21); [elaborate, then use
NORM.DIST(•,•,•,1)]
(d)[2] P(22 ≤ x ≤ 26); [elaborate, then use
NORM.DIST(•,•,•,1)]
(e)[3] P(20 ≤ x ≤ 28); [z‐scores, then use
NORM.S.DIST(•,1)]
(f)[1] x* so that...
A population of values has a normal distribution with μ = 128.5 and σ= 26.6 You...
A population of values has a normal distribution with μ = 128.5
and σ= 26.6 You intend to draw a random sample of size n=58
Find the probability that a single randomly selected value is
greater than 123.3. P(X > 123.3) =
Find the probability that a sample of size n= 58 is randomly
selected with a mean greater than 123.3. P(M > 123.3) =
For a normal population with μ = 40 and σ = 10, which of the following...
For a normal population with μ = 40 and σ = 10, which of the
following samples has the highest probability of being
obtained?
M = 38 for a sample of n = 4
M = 36 for a sample of n = 4
M = 38 for a sample of n = 100
M = 36 for a sample of n = 100
Suppose a population of scores x is normally distributed with μ = 16 and σ =...
Suppose a population of scores x is normally distributed with μ
= 16 and σ = 5. Use the standard normal distribution to find the
probability indicated. (Round your answer to four decimal
places.)
Pr(16 ≤ x ≤ 18.6)
Suppose a population of scores x is normally distributed with μ = 16 and σ =...
Suppose a population of scores x is normally
distributed with μ = 16 and σ = 5. Use the
standard normal distribution to find the probability indicated.
(Round your answer to four decimal places.)
Pr(16 ≤ x ≤ 18.3)
You may need to use the table of areas under the standard normal
curve from the appendix.
Also,
Use the table of areas under the standard normal curve to find
the probability that a z-score from the standard normal
distribution will...
The population of IQ scores form a normal distribution with a μ = 100 and a...
The population of IQ scores form a normal distribution with a μ
= 100 and a standard deviation of σ = 10. What is the probability
of obtaining a sample mean greater than M = 97, For a random sample
of n = 9 For a random sample of n = 25 people
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