Question

Problem 1. Let x be a random variable which approximately follows a normal distribution with mean µ = 1000 and σ = 200. Use the z-table, calculator, or computer software to find the following: Part A. Find P(x > 1500). Part B. Find P(x < 900). Part C. Find P(900 < x < 1500).

Answer #1

Problem 3. Let x be a discrete random variable with the
probability distribution given in the following table:
x = 50 100 150 200 250 300 350
p(x) = 0.05 0.10 0.25 0.15 0.15 0.20 0.10
(i) Find µ, σ 2 , and σ.
(ii) Construct a probability histogram for p(x).
(iii) What is the probability that x will fall in the interval
[µ − σ, µ + σ]?

A: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(z ≤ 1.11) =
B: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(z ≥ −1.24) =
C: Let z be a random variable with a standard normal
distribution. Find the indicated probability. (Round your answer to
four decimal places.)
P(−1.78 ≤ z...

Suppose that the random variable X follows a normal distribution
with mean 35 and variance 25.
a.) Calculate P(X > 37)
b.) Calculate P(32 < X < 38)
c.) Find the value of x so that P(X >x) is approximately
0.975

1. If the random variable Z has a standard normal
distribution, then P(1.17 ≤ Z ≤ 2.26) is
A) 0.1091
B) 0.1203
C) 0.2118
D) 0.3944
2. Choose from the Following: Gaussian Distribution, Empirical
Rule, Standard Normal, Random Variable, Inverse Normal, Normal
Distribution, Approximation, Standardized, Left Skewed, or
Z-Score.
The [_______] is also referred to as
the standard normal deviate or just the normal deviate.
3. The demand for a new product is
estimated to be normally distributed with μ...

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.

Let the random variable X follow a normal distribution
with µ = 22 and σ = 4. The probability is 0.90
that Xis 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.

A random variable X follows a normal distribution with
mean 135 and standard deviation 12. If a sample of size 10 is
taken, find P (x̅ < 137). (4 decimal places) Find the answer
using StatCrunch.

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.

Suppose the random variable X follows a normal distribution with
mean μ=52 and standard deviation σ=10.
Calculate each of the following.
In each case, round your response to at least 4 decimal
places.
a) P(X < 41) =
b) P(X > 61) =
c) P (47 < X < 67) =

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