Question

For a symmetric distribution with mean µ, the mean absolute deviation is the expected value MAD(X) = E(|X − µ|), of the absolute difference |X − µ|, which is strictly positive. The mean absolute deviation for the standard normal distribution is an integral 1 √ 2π Z ∞ −∞ |x| e −x 2/2 dx = p 2/π = 0.7979....

Part a: Find the MAD of the Bernoulli-1/2 distribution.

Part b: Find the MAD of the binomial distribution Bin(2, 1/2).

Part c: Find the mean absolute deviation of the normal distribution with variance 500?

Part d: Comment briefly on the relevance of the previous calculation to the number of heads in the Kerrich sequence.

Part e: True or false? MAD(3X + 7) = 3 × MAD(X).

Answer #1

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find 3 numbers that have the MAD= 1 (mean absolute
deviation)

A distribution with a mean of µ = 73 and a standard deviation of
σ = 8 is being transformed into a standardized distribution of µ =
100 and σ = 16. Find the new, standardized score for each of the
following values from the original population (plot each point on a
graph):
a. X = 80 b. X = 70
c. X = 65 d. X = 87

1. The absolute maximum value of f(x) = x 3 − 3x 2 + 12 on the
interval [−2, 4] occurs at x =? Show your work.
2.t. Let f(x) = sin x + cos2 x. Find the absolute maximum, and
absolute minimum value of f on [0, π]. Show your work.
Absolute maximum:
Absolute minimum:
3.Let f(x) = x √ (x − 2). The critical numbers of f are_______.
Show your work.

1. 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 = 14.3; σ = 3.5
P(10 ≤ x ≤ 26)=?
2.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 = 5.9; σ = 1.1
P(7 ≤ x ≤ 9)=?
3. Assume that x has a normal...

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.)
? = 6; ? = 2
P(5 ? x ? 8) =
B. 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.)
? = 13.8; ? = 3.1
P(8 ? x ? 12) =
C.Assume that x has...

Assume that x has a normal distribution with a mean of
1 and a standard deviation of 6.08.
Find the probability that x is between -7.33 and
5.74.

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).

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...

Given a random variable X following normal distribution with
mean of -3 and standard deviation of 4. Then random variable
Y=0.4X+5 is also normal.
(1)Find the distribution of Y, i.e. μy,σy
(2)Find the probabilities P(−4<X<0),P(−1<Y<0)
(3)Find the probabilities(let n size =8)
P(−4<X¯<0),P(3<Y¯<4)
(4)Find the 53th percentile of the distribution of X

5-1. Consider a random sample of size 36 from a normal
distribution (population) with a mean of 10 and a standard
deviation of 6. Which of the following statement is false?
(a) The mean of X¯ is 10. (b) The standard deviation of X¯ is 1.
(c) X¯ approximately follows a normal distribution. (d) There is an
incorrect statement in the alternatives above.
5-2. Let X1, . . . , X36 be a random sample from Bin(36, 0.5).
Which of...

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