Given that x is a Normal random variable with a mean of 10 and
standard
deviation of 4, find the following
probabilities: (6 points)
P(x<6.7)
P(x>12.5)
P(8.8<x<12.5)
1) Consider X a normal random variable with mean 4 and standard
deviation 2. Given that P(X<6)=0.841345 , compute P(2<= x
<= 6)
2)Consider X a normal random variable with mean 10 and standard
deviation 4. Given that P(x>9)=0.598708 and P(x<12)=0.691464
. Compute P(8< x < 11).
Let X be a random variable with mean ux=20 and standard
deviation x = 3 and let Y be a random variable with mean uy=28 and
standard deviation y =3. It is known that X and Y are independent
random variable. A new random variable U is created where U=Y-X.
what is the standard deviation of U?
Find the probability that the Normal random variable with mean
20 and standard deviation 3.2 will generate an outlier (outside the
inner fences) observation. Remember that the lower (upper) inner
fence is 1.5*IQR below (above) the first (third) quartile.
a.
0.0035
b.
0.0051
c.
0.0058
d.
0.0062
e.
0.0070
A normal random variable x has mean ? = 1.6
and standard deviation ? = 0.17. Find the probability
associated with each of the following intervals. (Round your
answers to four decimal places.)
(a)
1.00 < x < 1.20
(b)
x > 1.37
(c)
1.35 < x < 1.50
Suppose that X is a Normal random variable with mean 1.2 and
standard deviation 0.5.
a. Find a value a such that P(X?a)=0.10.
b. Find a value b such that P(X?b)=0.10.
c. Find a value c such that
P(1.2?c<X<1.2+c)=0.30.
A normal random variable x has mean ? = 1.6
and standard deviation ? = 0.17. Find the probability
associated with each of the following intervals. (Round your
answers to four decimal places.)
(a)
1.00 < x < 1.30
(b)
x > 1.32
(c)
1.25 < x < 1.50
Let Z be a normal random variable with mean µ = 0 and standard
deviation σ = 1, that is, Z ∼ N(0, 1). Find each of the
following:
(a) P(Z ≤ −1.13).
(b) P(Z ≥ −2.18).
(c) P(2.13 ≤ Z ≤ 2.57).
(d) P(−2.3 ≤ Z ≤ −1.1).
(e) P(0 ≤ Z ≤ 1.54).
(f) P(−1.54 ≤ Z ≤ 1.54).
(g) N(1.1243).
(h) N(−1.1243).
Given that x is a normal variable with mean 42 and standard
deviation 6.2, find the following probabilities. (Round your answer
to four decimal places.)
(a) P(x<= 60)
(b) P(x>= 50)
(c) P(50 <=x<= 60)