Question

A random sample of size *n* = 50 is selected from a
binomial distribution with population proportion

* p* = 0.8.

Describe the approximate shape of the sampling distribution of
*p̂*.

Calculate the mean and standard deviation (or standard error) of
the sampling distribution of *p̂*. (Round your standard
deviation to four decimal places.)

mean =

standard deviation =

Find the probability that the sample proportion *p̂* is
less than 0.9. (Round your answer to four decimal places.)

Answer #1

Solution :

Given that ,

p = 0.8

1 - p = 0.2

n = 50

The approximate shape of the sampling distribution of
*p̂*.

**
N (
,
)**

Mean:

= p = **0.8 **

standard deviation:

=
(p*(1-p))/n = (0.8*0.2)/50
= **0.0566**

P( < 0.9) = P(( - ) / < (0.9 - 0.8) / 0.0566)

= P(z < 1.77)

= 0.9616

**Probability = 0.9616**

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...

11. Random samples of size n = 80 were selected from a
binomial population with p = 0.2. Use the normal
distribution to approximate the following probability. (Round your
answer to four decimal places.)
P(p̂ ≤ 0.26)
12. Random samples of size n = 80 were selected from a
binomial population with p = 0.8. Use the normal
distribution to approximate the following probability. (Round your
answer to four decimal places.)
P(p̂ > 0.79)

Random samples of size n = 75 were selected from a
binomial population with p = 0.8. Use the normal
distribution to approximate the following probabilities. (Round
your answers to four decimal places.)
P(p̂ ≤ 0.83)
P(0.75 ≤ p̂ ≤ 0.83) =

Random samples of size n = 85 were selected from a
binomial population with p = 0.8. Use the normal
distribution to approximate the following probability. (Round your
answer to four decimal places.)
P(p̂ < 0.70) =

Suppose that a random sample of size 64 is to be selected from a
population with mean 40 and standard deviation 5.
(a) What are the mean and standard deviation of the sampling
distribution?
μx =
σx =
(b) What is the approximate probability that x will be
within 0.4 of the population mean μ? (Round your answer to
four decimal places.)
P =
(c) What is the approximate probability that x will differ
from μ by more than 0.8?...

suppose a random sample of n measurements is selected from a
binomial population with probability of success p=0.31. given
n=300.
describe the shape, and find the mean and the standard deviation of
the sampling distribution of the sample proportion

Suppose a random sample of n measurements is selected from a
binomial population with probability of success p = .38. Given n =
300, describe the shape, and find the mean and the standard
deviation of the sampling distribution of the sample
proportion, .

31) – (33): A random sample of size n = 40 is selected from a
population that has a proportion of successes p = 0.8.
31) Determine the mean proportion of the sampling distribution
of the sample proportion.
32) Determine the standard deviation of the sampling
distribution of the sample proportion, to 3 decimal places.
33) True or False? The sampling distribution of the sample
proportion is approximately normal.

Random samples of size n = 80 were selected from a
binomial population with p = 0.3. Use the normal
distribution to approximate the following probability. (Round your
answer to four decimal places.)
P(p̂ > 0.28) =

Random samples of size n = 90 were selected from a
binomial population with p = 0.3. Use the normal
distribution to approximate the following probability. (Round your
answer to four decimal places.)
P(0.26 ≤ p̂ ≤ 0.34) =

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