Question

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 the following statements is false?

(a) The mean of X¯ is 18. (b) The standard deviation of X¯ is 1/3. (c) The mean of P36 i=1 Xi is 648. (d) The standard deviation of P36 i=1 Xi is 18. (e) X¯ approximately follows a normal distribution.

Answer #1

Solution :

1) mean = = 10

standard deviation = = 6

n = 36

= = 10

= / n = 6 / 36 = 1

a) False statement is -(d) There is an incorrect statement in the alternatives above.

2)

b) approximately follows a normal distribution.

A random sample of size 36 is taken from a population with mean
µ = 17 and standard deviation σ = 4. The probability that the
sample mean is greater than 18 is ________.
a. 0.8413
b. 0.0668
c. 0.1587
d. 0.9332

A random sample of size n = 40 is selected from a binomial
distribution with population proportion p = 0.25. (a) What will be
the approximate shape of the sampling distribution of p̂?
approximately normal skewed symmetric Correct: Your answer is
correct. (b) What will be the mean and standard deviation (or
standard error) of the sampling distribution of p̂? (Round your
answers to four decimal places.) mean 0.25 Correct: Your answer is
correct. standard deviation 0.0685 Correct: Your answer...

a simple random sample of size 36 is taken from a normal
population with mean 20 and standard deivation of 15. What is the
probability the sample,neab,xbar based on these 36 observations
will be within 4 units of the population mean. round to the
hundreths placee

a simple random sample of size 36 is taken from a normal
population with mean 20 and standard deivation of 15. What is the
probability the sample,neab,xbar based on these 36 observations
will be within 4 units of the population mean. round to the
hundreths place

1.
Suppose that a random sample of size 36 is to be selected from a
population with mean 49 and standard deviation 9. What is the
approximate probability that will be within 0.5 of the
population mean?
a.
0.5222
b.
0.0443
c.
0.2611
d.
0.4611
e.
0.7389
2.
Suppose that x is normally distributed with a mean of 60 and a
standard deviation of 9. What is P(x 68.73)?
a.
0.834
b.
0.166
c.
0.157
d.
0.334
e.
0.170

1. A sample size of 49 drawn from a population with a mean of 36
and a standard deviation of 15 for the size of an English class.
What is the probability the class will have greater than 40
a. .9693
b. .4693
c. .0808
d. .0307
2. A sample size of 49 drawn from a population with a mean of 36
and a standard deviation of 15 for the size of an English class.
What is the probability the...

what is the approximate distribution of the mean of a random sample
size 36 frim a population whose mean and standard deviation are 20
and 12 respectively? why?

A random sample of size 13 was taken from a population with a
population mean 27 and a population standard deviation 5.
Determine each of the following about the sampling distribution
of the sample mean.
Awnser A, B, C
Round your answer to at least 3 decimal places where
appropriate.
a) μx_=
b) σx_=
c) Can we conclude that the sampling distribution of
the sample mean is approximately normal? Yes or No

Which of the following is NOT true regarding the sampling
distribution of the mean (Sample mean X-bar) for a large sample
size (sample size is greater than 36)? A. It has the same mean as
the population. B. It has a smaller standard deviation than the
population standard deviation. C. Approximately it follows a normal
distribution. D. It has the same distribution as the
population.

a. If X is a normal random variable with mean 10, and if the
probability that X is less than 11.54 is .72 then what is the
standard deviation of X?
1.75
3.50
4.20
12.25
b. If the standard deviation of a population is 36 and we take a
sample of size 9, then the standard error (the standard deviation
of the sample mean) is
12.00
3.00
108.00
4.00
c. According to the empirical rule, in a normal distribution
about...

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