Question 1

Under certain conditions where n is large enough,you can approximate the ____________________ distribution using the ____________________ distribution.

Accepted Answer

The answer of Under certain conditions where n is large...

Question 2

The standard deviation of $\hat { p }$ is also called the ____________________ of the sample proportion.

Accepted Answer

The answer of The standard deviation of \(\hat { p...

Question 3

The standard error of the sample proportion gets larger as:

Accepted Answer

The standard error of the sample proportion is maximized when p = 0.50 because the formula for the standard error of a proportion is sqrt[p(1-p)/n], where p is the proportion and n is the sample size. This expression is largest when p = 0.5, as the product p(1-p) reaches its maximum value at this point.

Question 4

The standard deviation of $\hat { p }$ is also called the:

Accepted Answer

The standard deviation of $\hat { p }$ is also called the standard error of the sample proportion. This measures the variability of sample proportions from sample to sample, and help to quantify the uncertainty in the estimate of the true population proportion.

Question 5

The continuity correction factor adds and subtracts the number ____________________ to/from x to find P(X = x).

Accepted Answer

The answer of The continuity correction factor adds and subtracts...

Question 6

What is the probability that you get more than 200 heads if you flip a coin 400 times?

Accepted Answer

The answer of What is the probability that you get...

Question 7

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is between 0.58 and 0.62 is:

Accepted Answer

First, we need to find the standard error of the sample proportion:
SE = sqrt(p(1-p)/n) = sqrt(0.6(1-0.6)/200) = 0.0387

Next, we need to standardize the sample proportion using the equation:
z = (p̂ - p) / SE

We want to find the probability that the sample proportion (p̂) is between 0.58 and 0.62, which can be rewritten as the probability that the standardized z-score is between:

z1 = (0.58 - 0.6) / 0.0387 = -0.515
z2 = (0.62 - 0.6) / 0.0387 = 0.515

Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-scores:
P(-0.515 < z < 0.515) = 0.8779 - 0.4399 = 0.4380

Therefore, the answer is choice A) 0.4380.

Question 8

Given that X is a binomial random variable with very large n,the binomial probability P(X $\le$ 5)is approximated by the area under a normal curve to the left of

Accepted Answer

The answer of Given that X is a binomial random...

Question 9

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is less than 0.58 is

Accepted Answer

We can use the central limit theorem to approximate the distribution of the sample proportion as a normal distribution with mean = population proportion = 0.60 and standard deviation = sqrt[(0.60)(0.40)/200] = 0.0387.

Then, we can standardize the sample proportion as follows:

(z-score) = (sample proportion - population proportion) / (standard deviation) = (0.58 - 0.60) / 0.0387 = -0.516

Using a standard normal distribution table, we can find the probability of getting a z-score less than -0.516. This probability is 0.281. Therefore, the answer is A) 0.281.

Question 10

The variance of $\hat { p }$ is ____________________.

Accepted Answer

The answer of The variance of $\hat { p }$...

Question 11

Given a binomial distribution with n trials and probability p of a success on any trial,a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if

Accepted Answer

The answer of Given a binomial distribution with n trials...

Question 12

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

Accepted Answer

The normal distribution can only be used to approximate the sampling distribution of the sample proportion if np and n(1-p) are both greater than or equal to 5. This ensures that there are enough observations in each category to make the approximation valid. Choice A is a commonly used guideline, but is not always necessary. Choice B is not relevant to the criteria for using the normal distribution. Choice C is also not a required condition for using the normal distribution, as the central limit theorem states that large enough sample sizes will result in approximately normal distributions regardless of the population distribution.

Question 13

To find the binomial probability P(X $\le$ 4)we calculate the area under the normal curve to the ____________________ (left/right)of the number ____________________.

Accepted Answer

The answer of To find the binomial probability P(X $\le$...

Question 14

The normal approximation to the binomial distribution gets better and better as ____________________ increases.

Accepted Answer

The answer of The normal approximation to the binomial distribution...

Question 15

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is greater than 0.58 is:

Accepted Answer

We can use the central limit theorem to approximate the distribution of the sample proportion. The mean of the sample proportion is equal to the population proportion, which is 0.60, and the standard deviation of the sample proportion can be calculated as:

sqrt(0.60*(1-0.60) / 200) = 0.039

To find the probability that the sample proportion is greater than 0.58, we can standardize the value using the z-score formula:

z = (0.58 - 0.60) / 0.039 = -0.51

Using a standard normal distribution table, we can find the probability that z is greater than -0.51:

P(z > -0.51) = 0.703

Therefore, the probability that the sample proportion is greater than 0.58 is:

1 - P(z > -0.51) = 1 - 0.703 = 0.297

The closest answer choice is B, which is 0.719 (which is 1 - 0.281). Therefore, the best choice is B.

Question 16

Suppose that the probability p of success on any trail of a binomial distribution equals 0.90.Then for which of the following number of trials,n,would the normal distribution provide a good approximation to the binomial distribution?

Accepted Answer

The answer of Suppose that the probability p of success...

Question 17

A sample of 250 observations is selected at random from an infinite population.Given that the population proportion is .25,the standard error of the sampling distribution of the sample proportion is:

Accepted Answer

The answer of A sample of 250 observations is selected...

Question 18

Suppose it is known that 60% of radio listeners at a particular college are smokers.A sample of 500 students from the college is selected at random.Approximate the probability that at least 280 of these students are radio listeners.

Accepted Answer

The answer of Suppose it is known that 60% of...

Question 19

The estimator of the probability of success in a binomial distribution is: ____________________.

Accepted Answer

The answer of The estimator of the probability of success...

Question 20

The expected value of $\hat { p }$ is ____________________.

Accepted Answer

The answer of The expected value of \(\hat { p...

Quiz 9: Sampling Distributions

Under certain conditions where n is large enough,you can approximate the distribution using the distribution.

The standard deviation of $\hat { p }$ is also called the ____________________ of the sample proportion.

The standard error of the sample proportion gets larger as:

The standard deviation of $\hat { p }$ is also called the:

The continuity correction factor adds and subtracts the number ____________________ to/from x to find P(X = x).

What is the probability that you get more than 200 heads if you flip a coin 400 times?

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is between 0.58 and 0.62 is:

Given that X is a binomial random variable with very large n,the binomial probability P(X $\le$ 5) is approximated by the area under a normal curve to the left of

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is less than 0.58 is

The variance of $\hat { p }$ is ____________________.

Given a binomial distribution with n trials and probability p of a success on any trial,a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

To find the binomial probability P(X $\le$ 4)we calculate the area under the normal curve to the (left/right)of the number .

The normal approximation to the binomial distribution gets better and better as ____________________ increases.

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is greater than 0.58 is:

Suppose that the probability p of success on any trail of a binomial distribution equals 0.90.Then for which of the following number of trials,n,would the normal distribution provide a good approximation to the binomial distribution?

A sample of 250 observations is selected at random from an infinite population.Given that the population proportion is .25,the standard error of the sampling distribution of the sample proportion is:

Suppose it is known that 60% of radio listeners at a particular college are smokers.A sample of 500 students from the college is selected at random.Approximate the probability that at least 280 of these students are radio listeners.

The estimator of the probability of success in a binomial distribution is: ____________________.

The expected value of $\hat { p }$ is ____________________.

Quiz 9: Sampling Distributions

Under certain conditions where n is large enough,you can approximate the ____________________ distribution using the ____________________ distribution.

The standard deviation of p^\hat { p }p^​ is also called the ____________________ of the sample proportion.

The standard error of the sample proportion gets larger as:

The standard deviation of p^\hat { p }p^​ is also called the:

The continuity correction factor adds and subtracts the number ____________________ to/from x to find P(X = x).

What is the probability that you get more than 200 heads if you flip a coin 400 times?

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is between 0.58 and 0.62 is:

Given that X is a binomial random variable with very large n,the binomial probability P(X ≤\le≤ 5) is approximated by the area under a normal curve to the left of

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is less than 0.58 is

The variance of p^\hat { p }p^​ is ____________________.

Given a binomial distribution with n trials and probability p of a success on any trial,a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if

As a general rule,the normal distribution is used to approximate the sampling distribution of the sample proportion only if:

To find the binomial probability P(X ≤\le≤ 4)we calculate the area under the normal curve to the ____________________ (left/right)of the number ____________________.

The normal approximation to the binomial distribution gets better and better as ____________________ increases.

A sample of size 200 is taken at random from an infinite population.Given that the population proportion is 0.60,the probability that the sample proportion is greater than 0.58 is:

Suppose that the probability p of success on any trail of a binomial distribution equals 0.90.Then for which of the following number of trials,n,would the normal distribution provide a good approximation to the binomial distribution?

A sample of 250 observations is selected at random from an infinite population.Given that the population proportion is .25,the standard error of the sampling distribution of the sample proportion is:

Suppose it is known that 60% of radio listeners at a particular college are smokers.A sample of 500 students from the college is selected at random.Approximate the probability that at least 280 of these students are radio listeners.

The estimator of the probability of success in a binomial distribution is: ____________________.

The expected value of p^\hat { p }p^​ is ____________________.

Under certain conditions where n is large enough,you can approximate the distribution using the distribution.

The standard deviation of $\hat { p }$ is also called the ____________________ of the sample proportion.

The standard deviation of $\hat { p }$ is also called the:

Given that X is a binomial random variable with very large n,the binomial probability P(X $\le$ 5) is approximated by the area under a normal curve to the left of

The variance of $\hat { p }$ is ____________________.

To find the binomial probability P(X $\le$ 4)we calculate the area under the normal curve to the (left/right)of the number .

The expected value of $\hat { p }$ is ____________________.