Question

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?________

Answer #1

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

Suppose we know that a random variable X has a population mean µ
= 100 with a standard deviation σ = 30. What are the following
probabilities?
a. The probability that X > 102 when n = 1296.
b. The probability that X > 102 when n = 900.
c. The probability that X > 102 when n = 36.

8. A random sample is obtained from a
normal population with a mean of µ = 80 and a standard deviation of
σ = 8. Which of the following outcomes is more likely? Explain your
answer.
A. A
sample mean greater than 86 for a sample of n = 4 scores.
B. A
sample mean greater than 84 for a sample of n = 16 scores.
9. The distribution of SAT scores is
normal with a mean of...

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.

__________ For a continuous random variable x, the area
under the probability distribution curve between any two x-values
is always _____.
Greater than 1 B) less than
zero C) equal to 1 D) in the
range zero to 1, inclusive
_________For a continuous random variable x, the total
area under the probability distribution curve of x is always
______?
Less
than1 B)
greater than
1
C) equal to
1
D) 0.5
___________ The probability that a continuous random
variable x...

A normal random variable x has an unknown mean and standard
deviation. The probability that x exceeds 4 is 0.975, and the
probability that x exceeds 5 is 0.95. Find μ and σ.

According to a study, the random variable, at least X,
expressing the length of the fish endemic to a lake follows a
normal distribution with mean µ = 20cm and standard deviation σ =
4cm. a) A fish is fishing by the lake. What is the probability that
its length is greater than 18cm but does not exceed 24cm? b)
Determine a symmetric mean of the X interval whose lengths are 95%
of the lake's fish. c) Angling 4 fish...

a.) Assume that x has a normal distribution with the
specified mean and standard deviation. Find the indicated
probability. (Round your answer to four decimal places.)
μ = 4.4; σ = 2.2
P(3 ≤ x ≤ 6) =
b.) Consider a normal distribution with mean 34 and standard
deviation 2. What is the probability a value selected at random
from this distribution is greater than 34? (Round your answer to
two decimal places.)
c.) Assume that x has a normal...

(squared mean error) The expected value of the random variable X
is µ = 5 and the standard deviation σ = 2.
The aim is to predict the unknown value of the random variable with
a constant and a prediction error
measured by the formula g (a) = E((X - a)2)
.
(a) Determine the value of constant a for which the prediction
error is the lowest.
(b) Determine the minimum value of the prediction error.
(Hint: By applying the...

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