Question

- Let x bar be the mean of a random sample of n = 36 currents (in milliamperes) in a strip of wire in which each measurement has a mean of 16 and a variance of 6. X bar has an approximate normal distribution, find P(12.5 < x bar < 15.6) .

Answer #1

Suppose a random sample of n=36 measurements is selected from a
population with mean u=256 and variance o^2=144.
a. Describe the sampling distribution of the sample mean x bar.
(Hint: describe the shape, calculate the mean and the standard
deviation of the sampling distribution of x bar.
b. What is the probability that the sample mean is greater than
261?

Suppose the curent measurements in a strip of wire follow a
normal distribution with a mean
of 10 milliamperes (mA) and a standard deviation of 2 mA.
(a) Find the probability that the measurement on a random strip of
wire exceeds 13 mA. (10
pts.)
(b) Find the probability that the measurement on a random strip
of wire is between 5.3 mA and
12.8 mA. (10 pts.)
(c) The wire is considered to be defective if its current
measurement is...

approximate p{23<x<31} wherr X us the mean of a random sample
of size 36 with a distribution with mesn u=35 and varience o^2=
16

Let ? ̅ and ?2 be the mean and variance of a random sample of
size 16 from a normal distribution N(4, 128). Find (a) ?(5 < ? ̅
< 8) (b) ?(200 < ?2 < 262.4)

Problem 6. A random variable x has a Normal distribution with an
unknown mean and a standard deviation of 12. Suppose that we take a
random sample of size n = 36 and ﬁnd a sample mean of "x-bar" = 98.
What is a 95% conﬁdence interval for the mean of x?

Let the random variable X follow a Normal distribution with
variance σ2 = 625.
A random sample of n = 50 is obtained with a sample mean, X-Bar
of 180.
What is the probability that μ is between 198 and 211?
What is Z-Score1 for μ greater than 198?

Let X be the mean of a random sample of size n from a N(θ, σ2)
distribution,
−∞ < θ < ∞, σ2 > 0. Assume that σ2 is known. Show that
X
2 − σ2
n is an
unbiased estimator of θ2 and find its efficiency.

We have a sample of size n = 36 with mean x with bar on top
space equals 12. If population standard deviation, sigma equals 2,
what is the upper limit of 95% confidence interval (zα/2=1.96) of
population mean µ?

Let X be a binomial random variable with n =
400 trials and probability of success p = 0.01. Then the
probability distribution of X can be approximated by
Select one:
a. a Hypergeometric distribution with N =
8000, n = 400, M = 4.
b. a Poisson distribution with mean 4.
c. an exponential distribution with mean 4.
d. another binomial distribution with n =
800, p = 0.02
e.
a normal distribution with men 40 and variance 3.96.

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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