Question

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.

Answer #1

X follows normal distribution with mean = 18 and = 11

Probability that X is greater than 10 and less than 17 = P(10<X<17) = P(X<17) - P(X<10)

P(X<17)

Z-score for 17 = (17-)/ = (17-18)/3.3166 = -0.30

From standard normal tables, P(Z<-0.30) = 0.3821

P(X<17) = P(Z<-0.30) = 0.3821

P(X<10)

Z-score for 10 = (10-)/ = (10-18)/3.3166 = -2.41

From standard normal tables, P(Z<-2.41) = 0.0080

P(X<10) = 0.0080

P(10<X<17) = P(X<17) - P(X<10) = 0.3821 - 0.0080=0.3741

Probability that X is greater than 10 and less than 17 = 0.3741

Let the random variable X follow a normal distribution with µ =
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less than 15.

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?
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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.

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Let the random variable X follow a normal distribution
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For
Questions 6 - 8, let the random variable X follow a Normal
distribution with variance σ2 = 625.
Q6. A random sample of n = 50 is obtained with a sample mean, X-Bar
of 180.
What is
the probability that population mean μ is greater than 190?
a.
What is Z-Score for μ greater than 190 ==>
b.
P[Z > Z-Score] ==>
Q7. What
is the probability that μ is between 198 and 211?
a. What
is Z-Score1 for...

1) let X be a continuous random
variable that has a normal distribution with a mean of 40 and a
standard deviation of 5. Find the probability that X
assumes a value:
a. between 32 and
35 b. between 41 and 50
c. greater than
43 d. less than 49

If X is a normal random variable that has a mean of µ = 20 and a
standard deviation σ = 2, (a) the standardized value of X=16 is
_________. (b) What is the probability that X is less than or equal
to 16? __________ (c) What is the probability that X is greater
than 16? __________ (d) What is the probability that X is equal to
16?________

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).

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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