Question

Suppose x is a normally distributed random variable with μ=30 and σ=5. Find a value x 0of the random variable x. (Round to two decimal places as needed.)

p(x >x 0): 0.95

Answer #1

Note that:

If, X ~ Normal , then,

We have to use software or Standard Normal table to find its value, I will use R studio here.

R code: pnorm(z)

Also let, , kth quantile of N(0,1)

R code: qnorm(k)

Here, X ~ Normal()

So,

R output:

> qnorm(0.05) [1] -1.644854

Suppose x is a normally distributed random variable with μ=15
and σ=2. Find each of the following probabilities. (Round to three
decimal places as needed.)
a. P(x≥17.5)
b. P(x≤14.5)
c. P(15.8 ≤ x ≤ 19.48)
d. P(10.58 ≤ x ≤17.4)

Suppose x is a normally distributed random variable with μ=33
and σ=4
Find a value x0 of the random variable x that satisfies the
following equations or statements.
a. 10% of the values of x are less than x0.
b. 1% of the values of x are greater than x0.

Suppose a population of scores x is normally distributed with μ
= 30 and σ = 12. Use the standard normal distribution to find the
probability indicated. (Round your answer to four decimal
places.)
Pr(24 ≤ x ≤ 42)

Suppose that the random variable x is normally distributed with
μ = 1,000 and standard deviation σ = 100.
Find each of the following probabilities. Round your z-score
calculations to 2 decimal places. Provide your probability answers
to 4 decimal places.
z-score
probability
P( x > 1257)
P( x < 1035)
P( x ≤ 700)
z-score
z-score
probability
P(1000 ≤ x ≤ 1200)
P(812 ≤ x ≤ 913)

Suppose X is a normal random variable with μ =
60 and σ = 5. Find the values of the following
probabilities. (Round your answers to four decimal places.)
(a) P(X < 65)
(b) P(X > 46)
(c) P(58 < X <
67)
You may need to use the appropriate table in the Appendix of Tables
to answer this question.

1. Assume the random variable x is normally distributed with
mean μ=85 and standard deviation σ=5. P(69 < x <83)
Find the indicated probability.

A population is normally distributed with
μ=200
and
σ=10.
a.
Find the probability that a value randomly selected from this
population will have a value greater than
210.
b.
Find the probability that a value randomly selected from this
population will have a value less than
190.
c.
Find the probability that a value randomly selected from this
population will have a value between
190
and
210.
a. P(x>210)=
(Round to four decimal places as needed.)
b. P(x<190)=
(Round to...

Suppose X is a normal random variable with μ =
390 and σ = 40. Find the values of the following
probabilities. (Round your answers to four decimal places.)
(a) P(X < 452)
(b) P(430 < X <
474)
(c) P(X > 430)

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

A random variable x is normally
distributed: x~N(μ=74, σ=4.3).
What percent of the population values will be greater than
77.9?
Enter in percent form (without %), correct to two digits after
the decimal point:
We want to change μ, without changing σ, such that in this new
distribution, 30% of the values would be higher than 77.9.
Determine the new value of μ.
Give the answer correct to two digits after the decimal
point:

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