Question

Let the random variable *X* follow a normal distribution
with *µ* = 22 and *σ* = 4. The probability is 0.90
that *X*is in the symmetric interval about the mean between
two numbers, L and U (L is the smaller of the two numbers and U is
the larger of the two numbers). Calculate U.

Answer #1

P ( a < X < b ) = 0.9

Dividing the area 0.9 in two parts we get 0.9/2 = 0.45

since 0.5 area in normal curve is above and below the mean

Area below the mean is a = 0.5 - 0.45

Area above the mean is b = 0.5 + 0.45

Looking for the probability 0.05 in standard normal table to
calculate critical value Z = -1.64

Looking for the probability 0.95 in standard normal table to
calculate critical value Z = 1.64

-1.64 = ( X - 22 ) / 4

a = 15.44

1.64 = ( X - 22 ) / 4

b = 28.56

P ( 15.44 < X < 28.56 ) = 0.9

U = 28.56

Let the random variable X follow a normal distribution with µ =
18 and σ = 4. The probability is 0.99 that X is in the symmetric
interval about the mean between two numbers, L and U (L is the
smaller of the two numbers and U is the larger of the two numbers).
Calculate L.

5.19) Let the random variable X follow a normal distribution
with U(mu) = 50 and S2 = 64.
e. The probability is 0.05 that X is in the symmetric
interval about the mean between which two
numbers?

Let the random variable X follow a normal distribution with μ =
60 and σ^2=64.
a.
Find the probability that X is greater than 70.
b.
Find the probability that X is greater than 45 and less than
74.
c.
Find the probability that X is less than 65.
d.
The probability is 0.2 that X is greater than what
number?
e.
The probability is 0.05 that X is in the symmetric interval
about the mean between which two numbers?

Let the random variable X follow a normal distribution with
muμequals=4040 and sigmaσ2equals=6464. a. Find the probability that
X is greater than 5050. b. Find the probability that X is greater
than 2020 and less than 5252. c. Find the probability that X is
less than 4545. d. The probability is 0.30.3 that X is greater than
what number? e. The probability is 0.070.07 that X is in the
symmetric interval about the mean between which two numbers?

Let the random variable X follow a normal distribution with µ =
19 and σ2 = 8. Find the probability that X is greater than 11 and
less than 15.

Let the random variable X follow a normal distribution with µ =
18 and σ2 = 11. Find the probability that X is greater than 10 and
less than 17.

Let the random variable X follow a Normal distribution with
variance σ2 = 625.
A random sample of n = 50 is obtained with a sample mean, X-Bar
of 180.
What is the probability that μ is between 198 and 211?
What is Z-Score1 for μ greater than 198?

2. Let X be a Normal random variable with µ = 11 and σ 2 = 49.
You may refer to the tables at the end of our textbook.
(a) Calculate P(X2 > 100).
(b) Calculate the hazard rate function at 18, λ(18) and at 25,
λ(25).

Let x be a continuous random variable that has a normal
distribution with μ=85 and σ=12. Assuming n/N ≤ 0.05, find the
probability that the sample mean, x¯, for a random sample of
18taken from this population will be between 81.7 and 90.4.
Round your answer to four decimal places.

2. Let the random variable Z follow a standard normal
distribution, and let z1 be a possible value of Z that is
representing the 10th percentile of the standard normal
distribution. Find the value of z1. Show your
calculation.
A. 1.28
B. -1.28
C. 0.255
D. -0.255
3. Given that X is a normally distributed random variable with a
mean of 52 and a standard deviation of 2, the probability that X is
between 48 and 56 is: Show your...

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