Question 1

A(n) is a distribution of means obtained from
samples of a specific size taken from a population.

Accepted Answer

The answer of A(n) is a distribution of means obtained...

Question 2

$X$ is a normally distributed random variable with a mean of 10 and a standard deviation of $4.0$. Find the value of $X$ for which $70.54 \%$ of the area under the distribution curve lies right of it. (Note: the diagram is not necessarily to scale.)

Accepted Answer

The answer of $X$ is a normally distributed random variable...

Question 3

$X$ is a normally distributed random variable with a standard deviation of $2.00$. Find the mean of $X$ if $12.71 \%$ of the area under the distribution curve lies to the right of $10.28$. (Note: the diagram is not necessarily to scale.)

Accepted Answer

The answer of $X$ is a normally distributed random variable...

Question 4

$X$ is a normally distributed random variable with a mean of $7.0$ and a standard deviation of 3.00. Find the value $x$ such that $P ( X < x )$ is equal to $0.86$. (Note: the diagram is not necessarily to scale.)

Accepted Answer

The answer of $X$ is a normally distributed random variable...

Question 5

The difference between a sample mean and the population mean may be referred to as .

Accepted Answer

Sampling error is the difference between a sample statistic (such as sample mean) and the corresponding population parameter (such as population mean). This error arises because the sample is only a part of the population, and there's a chance that the sample might not perfectly represent the population.

Question 6

$X$ is a normally distributed random variable with a mean of $4.0$. Find the standard deviation of the distribution if $59.10 \%$ of the data lies to the right of $3.54$. (Note: the diagram is not necessarily to scale.)

Accepted Answer

The answer of $X$ is a normally distributed random variable...

Question 7

$X$ is a normally distributed random variable with a standard deviation of $3.50$. Find the mean of $X$ when $64.8 \%$ of the area lies to the left of $5.33$. (Note: the diagram is not necessarily to scale.)

Accepted Answer

The answer of $X$ is a normally distributed random variable...

Question 8

For a normal distribution with a mean of 7 and a standard deviation of 6 , the value has a $z$ value of

Accepted Answer

The z-value is calculated as (x - mean) / standard deviation. In this case, the z-value is (7 - 7) / 6 = 0.

Question 9

In the distribution shown, state the mean and standard deviation. Hint: The vertical lines are 1 standard deviation apart.

Accepted Answer

The answer of In the distribution shown, state the mean...

Question 10

The data shown represent quiz scores from Ms. Mayer's 5th grade class. Use the Pearson coefficient to check for skewness.
21 25 9 21 23 22 22 15 23 22 16 11 20 20 17 22 21

Accepted Answer

The answer of The data shown represent quiz scores from...

Question 11

For a normal distribution with a mean of 13 and a standard deviation of 6 , the value has a $z$ value of

Accepted Answer

The answer of For a normal distribution with a mean...

Question 12

In order to have the standard error of the mean be 15, one would need to take samples from a normally distributed population with a standard deviation of 45.

Accepted Answer

The answer of In order to have the standard error...

Question 13

If the standard deviation of a normally distributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is

Accepted Answer

The standard error of the mean is calculated as the standard deviation of the population divided by the square root of the sample size. Here, it is 55.0 / sqrt(25) = 55.0 / 5 = 11.0.

Question 14

If the average price of a new one-family home is $243,500 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will
Build to satisfy the middle 80% of the market. Assume that the variable is normally
Distributed.

Accepted Answer

To find the minimum and maximum prices for the middle 80% of the market, we need to look at the properties of the normal distribution. The middle 80% corresponds to the 10th percentile to the 90th percentile. Using the standard normal distribution, these percentiles correspond to z-scores of approximately -1.28 and +1.28, respectively. To find the actual values, we use the formula for a value in a normal distribution: X = μ + zσ, where μ is the mean, σ is the standard deviation, and z is the z-score.For the 10th percentile (minimum price):X = $243,500 + (-1.28)($15,000) = $243,500 - $19,200 = $224,300.For the 90th percentile (maximum price):X = $243,500 + (1.28)($15,000) = $243,500 + $19,200 = $262,700.Therefore, the minimum and maximum prices to satisfy the middle 80% of the market are $224,300 and $262,700, respectively.

Question 15

A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7.5 years. If a person
In Africa is selected at random, what is the probability that the person will die before the
Age of 65?

Accepted Answer

To find the probability that a person will die before the age of 65, we use the Z-score formula: Z = (X - μ) / σ, where X is the value of interest (65 years), μ is the mean (53 years), and σ is the standard deviation (7.5 years). Plugging in the values, we get Z = (65 - 53) / 7.5 = 12 / 7.5 = 1.6. Looking up a Z-score of 1.6 in the standard normal distribution table gives us a probability of approximately 0.945 or 94.5%.

Question 16

$X$ is a normally distributed random variable with a mean of $11.00$. If the probability that $X$ is less than $11.88$ is $0.67$ (as shown below), then what is the standard deviation of (Note: the diagram is not necessarily to scale.)

Accepted Answer

The answer of $X$ is a normally distributed random variable...

Question 17

What is the $z$ value such that $50 \%$ of the total area under the standard normal distribution curved lies to the right of it?

Accepted Answer

The answer of What is the $z$ value such that...

Question 18

The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are normally distributed with a standard deviation of 1.5 feet, find the probability
That a tree is less than 12.5 feet tall.

Accepted Answer

The answer of The average height of flowering cherry trees...

Question 19

In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation
Of 200, what is the lowest possible score a student needs to qualify for acceptance into
The university?

Accepted Answer

To find the lowest possible score to be in the top 5%, we use the z-score formula for the 95th percentile, since the top 5% would start from the 95th percentile upwards. The z-score for the 95th percentile is approximately 1.645. Using the z-score formula: Z = (X - μ) / σ, where Z is the z-score, X is the score, μ is the mean, and σ is the standard deviation, we can solve for X: 1.645 = (X - 1000) / 200. Solving for X gives us X = 1.645 * 200 + 1000 = 329 + 1000 = 1329. Since test scores are whole numbers, rounding up gives us 1330 as the lowest possible score to be in the top 5%.

Question 20

The following formula can be used to find the specific value of the variable in a data set t. corresponds to a particular value of the standard normal variable:
$$X = z \cdot \sigma + \mu$$

Accepted Answer

This formula is used to find a specific value $X$ in a data set, where $z$ is the value of the standard normal variable, $\sigma$ is the standard deviation of the data set, and $\mu$ is the mean of the data set.

Quiz 6: The Normal Distribution

A(n) is a distribution of means obtained from samples of a specific size taken from a population.

$X$ is a normally distributed random variable with a mean of $7.0$ and a standard deviation of 3.00. Find the value $x$ such that $P ( X < x )$ is equal to $0.86$ . (Note: the diagram is not necessarily to scale.)

The difference between a sample mean and the population mean may be referred to as .

For a normal distribution with a mean of 7 and a standard deviation of 6 , the value has a $z$ value of

The data shown represent quiz scores from Ms. Mayer's 5th grade class. Use the Pearson coefficient to check for skewness. 21 25 9 21 23 22 22 15 23 22 16 11 20 20 17 22 21

For a normal distribution with a mean of 13 and a standard deviation of 6 , the value has a $z$ value of

In order to have the standard error of the mean be 15, one would need to take samples from a normally distributed population with a standard deviation of 45.

If the standard deviation of a normally distributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is

If the average price of a new one-family home is $243,500 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will Build to satisfy the middle 80% of the market. Assume that the variable is normally Distributed.

A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7.5 years. If a person In Africa is selected at random, what is the probability that the person will die before the Age of 65?

$X$ is a normally distributed random variable with a mean of $11.00$ . If the probability that $X$ is less than $11.88$ is $0.67$ (as shown below) , then what is the standard deviation of (Note: the diagram is not necessarily to scale.)

What is the $z$ value such that $50 \%$ of the total area under the standard normal distribution curved lies to the right of it?

The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are normally distributed with a standard deviation of 1.5 feet, find the probability That a tree is less than 12.5 feet tall.

In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation Of 200, what is the lowest possible score a student needs to qualify for acceptance into The university?

The following formula can be used to find the specific value of the variable in a data set t. corresponds to a particular value of the standard normal variable: $X = z \cdot \sigma + \mu$

Quiz 6: The Normal Distribution

A(n) is a distribution of means obtained from samples of a specific size taken from a population.

XXX is a normally distributed random variable with a mean of 10 and a standard deviation of 4.04.04.0 . Find the value of XXX for which 70.54%70.54 \%70.54% of the area under the distribution curve lies right of it. (Note: the diagram is not necessarily to scale.)

XXX is a normally distributed random variable with a standard deviation of 2.002.002.00 . Find the mean of XXX if 12.71%12.71 \%12.71% of the area under the distribution curve lies to the right of 10.2810.2810.28 . (Note: the diagram is not necessarily to scale.)

XXX is a normally distributed random variable with a mean of 7.07.07.0 and a standard deviation of 3.00. Find the value xxx such that P(X<x) P ( X < x ) P(X<x) is equal to 0.860.860.86 . (Note: the diagram is not necessarily to scale.)

The difference between a sample mean and the population mean may be referred to as .

XXX is a normally distributed random variable with a mean of 4.04.04.0 . Find the standard deviation of the distribution if 59.10%59.10 \%59.10% of the data lies to the right of 3.543.543.54 . (Note: the diagram is not necessarily to scale.)

XXX is a normally distributed random variable with a standard deviation of 3.503.503.50 . Find the mean of XXX when 64.8%64.8 \%64.8% of the area lies to the left of 5.335.335.33 . (Note: the diagram is not necessarily to scale.)

For a normal distribution with a mean of 7 and a standard deviation of 6 , the value has a zzz value of

In the distribution shown, state the mean and standard deviation. Hint: The vertical lines are 1 standard deviation apart.

The data shown represent quiz scores from Ms. Mayer's 5th grade class. Use the Pearson coefficient to check for skewness. 21 25 9 21 23 22 22 15 23 22 16 11 20 20 17 22 21

For a normal distribution with a mean of 13 and a standard deviation of 6 , the value has a zzz value of

In order to have the standard error of the mean be 15, one would need to take samples from a normally distributed population with a standard deviation of 45.

If the standard deviation of a normally distributed population is 55.0 and we take a sample of size 25, then the standard error of the mean is

If the average price of a new one-family home is $243,500 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will Build to satisfy the middle 80% of the market. Assume that the variable is normally Distributed.

A recent study found that the life expectancy of a people living in Africa is normally distributed with an average of 53 years with a standard deviation of 7.5 years. If a person In Africa is selected at random, what is the probability that the person will die before the Age of 65?

XXX is a normally distributed random variable with a mean of 11.0011.0011.00 . If the probability that XXX is less than 11.8811.8811.88 is 0.670.670.67 (as shown below) , then what is the standard deviation of (Note: the diagram is not necessarily to scale.)

What is the zzz value such that 50%50 \%50% of the total area under the standard normal distribution curved lies to the right of it?

The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are normally distributed with a standard deviation of 1.5 feet, find the probability That a tree is less than 12.5 feet tall.

In order to be accepted into a certain top university, applicants must score within the top 5% on the SAT exam. Given that the exam has a mean of 1000 and a standard deviation Of 200, what is the lowest possible score a student needs to qualify for acceptance into The university?

The following formula can be used to find the specific value of the variable in a data set t. corresponds to a particular value of the standard normal variable: X=z⋅σ+μX = z \cdot \sigma + \muX=z⋅σ+μ

$X$ is a normally distributed random variable with a mean of $7.0$ and a standard deviation of 3.00. Find the value $x$ such that $P ( X < x )$ is equal to $0.86$ . (Note: the diagram is not necessarily to scale.)

For a normal distribution with a mean of 7 and a standard deviation of 6 , the value has a $z$ value of

For a normal distribution with a mean of 13 and a standard deviation of 6 , the value has a $z$ value of

$X$ is a normally distributed random variable with a mean of $11.00$ . If the probability that $X$ is less than $11.88$ is $0.67$ (as shown below) , then what is the standard deviation of (Note: the diagram is not necessarily to scale.)

What is the $z$ value such that $50 \%$ of the total area under the standard normal distribution curved lies to the right of it?

The following formula can be used to find the specific value of the variable in a data set t. corresponds to a particular value of the standard normal variable: $X = z \cdot \sigma + \mu$