Question

A standard normal random variable is a random variable that is normally distributed with mean equal to 1 and standard deviation equal to 1.

Group of answer choices

True

False

Answer #1

A standard normal random variable is a random variable that is normally distributed with mean equal to 0 and standard deviation equal to 1

So, the above statement given is FALSE

The normal distribution is a continuous probability distribution. This has several implications for probability.

- The total area under the normal curve is equal to 1.
- The probability that a normal random variable
*X*equals any particular value is 0. - The probability that
*X*is greater than*a*equals the area under the normal curve bounded by*a*and plus infinity (as indicated by the*non-shaded*area in the figure below). - The probability that
*X*is less than*a*equals the area under the normal curve bounded by*a*and minus infinity (as indicated by the*shaded*area in the figure below).

X is a normally distributed random variable with a mean of 4.0.
Find the standard deviation of the distribution if 59.10% of the
data lies to the right of 3.54. (Note: the diagram is not
necessarily to scale.) Group of answer choices
A. 1.0
B. 2.0
C. 0.5
D. 1.3

A random variable is normally distributed with a mean of
μ = 60
and a standard deviation of
σ = 5.
What is the probability the random variable will assume a value
between 45 and 75? (Round your answer to three decimal places.)

A random variable is normally distributed with a mean of μ = 70
and a standard deviation of σ = 10
What is the probability the random variable will assume a value
between 50 and 90? (Round your answer to three decimal places.)
What is the probability the random variable will assume a value
between 60 and 80? (Round your answer to three decimal places.)

assume the random variable X is normally distributed with mean
50 in standard deviation =7 compute the probability, be sure to
draw a normal curve with area corresponding to the probability
shaded
P(54 less than eaual to X less than equal to 66) =

A random variable is normally distributed with a mean of μ=50
and a standard deviation of σ = 5.
a) Sketch a normal curve for the probability density function.
Label the horizontal axis with values of 35, 40, 45, 50, 55, 60,
and 65.
b) What is the probability the random variable will assume a
value between 45 and 55?
c) What is the probability the random variable will assume a
value between 40 and 60?
d) Draw a graph...

A random variable is normally distributed with a mean of
15 and a standard deviation of 2.5.
Find P(X > 20)
Find P(X < 16.25)
Find P(13.125 < X < 17)

A random variable is normally distributed. It has a mean of 245
and a standard deviation of 21. a.) For a sample of size 10, state
the mean of the sample mean and the standard deviation of the
sample mean. b.) For a sample of size 10, find the probability that
the sample mean is more than 230.

1.Suppose X is a random variable that is normally distributed with mean 5 and standard deviation 0.4. If P (X≤X0) = P (Z≤1.3). What is the value of X0.?
Select one:
2.00
5.52
6.90
4.48
2.Suppose X is a random variable that is normally distributed with a mean of 5. If P (X≤3) = 0.2005, what is the value of the standard deviation?
Select one:
σ = 2.38
σ = −2
σ = 1.38
σ = 2

Let x be a normal random variable with mean equal to 40 and
standard deviation equal to 5
a) P(x>55)=?
b) P(x<49)=?

A random variable is normally distributed with a mean of
80 and a standard deviation of 6.
a) Find P(X < 75.5)
b) Find P(X > 82)
c) Find P(77 < X < 84.8)

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