Using the diagram, which two planes would hg intersect in ?

MNM Corporation gives each of its 500 employees an aptitude test. The scores on the test are normally distributed with a mean of

djyliett [7]

Answer:

Q1: $P(\bar X$

Q2: $0.6 - 1.96 \sqrt{\frac{0.6(1-0.6)}{100}}=0.504$

$0.6 + 1.96 \sqrt{\frac{0.6(1-0.6)}{100}}=0.696$

And the 95% confidence interval would be given (0.504;0.696).

We are confident 95% that about 50.4% to 69.6% of people would like the cereal

Q3: $n=\frac{0.5(1-0.5)}{(\frac{0.09}{1.96})^2}=118.57$

And rounded up we have that n=119

Step-by-step explanation:

Q1 :MNM Corporation gives each of its 500 employees an aptitude test. The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15. A simple random sample of 36 is taken from the population of 500 employees. What is the probability that the average aptitude test score in the sample will be less than 78.69?

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(75,15)$

Where $\mu=75$ and $\sigma=15$

The distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=75, \frac{\sigma}{\sqrt{n}}=\frac{15}{\sqrt{36}}=2.5)$

For this case we want this probability:

$P(\bar X$

And we can use the z score given by:

$z= \frac{\bar X -\mu}{\sigma_{\bar X}}$

$P(\bar X$

Q2: A new brand of breakfast cereal is being market tested. One hundred boxes of the cereal were given to consumers to try. The consumers were asked whether they liked or disliked the cereal. Their responses are provided below.

Liked =60, Disliked =40 , Total =100

Construct a 95% confidence interval for the true proportion of people who will like the cereal. Interpret the practical meaning of this interval estimate, in plain English.

n=100 represent the random sample taken

X=60 represent the people liked with the cereal

$\hat p=\frac{60}{100}=0.6$ estimated proportion of people who liked the cereal

$\alpha=0.05$ represent the significance level (no given, but is assumed)

Confidence =95% or 0.95

p= population proportion of people drivers claimed they always buckle up

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.6 - 1.96 \sqrt{\frac{0.6(1-0.6)}{100}}=0.504$

$0.6 + 1.96 \sqrt{\frac{0.6(1-0.6)}{100}}=0.696$

And the 95% confidence interval would be given (0.504;0.696).

We are confident 95% that about 50.4% to 69.6% of people would like the cereal

Q3: Assume that nothing is known about the population proportion. With a .95 probability, how large of a sample needs to be taken to provide a margin of error of 9% or less?

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.09$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.5 since we don't have other info provided to assume a different value. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.09}{1.96})^2}=118.57$

And rounded up we have that n=119

5 0

3 years ago

Explain how to create a graph to model the relationship between the 2 quantities in the table. A 2-column table with 4 rows. Col

azamat

Answer:

Sample Response:Use the values in the table to create ordered pairs. Label the x-axis with the independent variable, hours. Label the y-axis with the dependent variable, dollars. Plot the ordered pairs on the graph. If the variables can be represented as fractional parts you can draw a line from the origin that connects the points.

Step-by-step explanation:

I took one for the team D:

4 0

3 years ago

The temperature is 58° F. It gets warmer by h degrees and reaches to 65° F. Find h.

Aleks [24]

Answer:

h = 7 degrees

Step-by-step explanation:

To find <em>h</em>, we know that it is positive because it increases in value, not decreases:

h = 65 - 58

h = 7

7 0

3 years ago

Read 2 more answers

Hill in the blank: Type your answer in the box and then clichWhat is the value of n?144eAnswer:

Inessa05 [86]

The correct answer is $95$ °.

To solve for $n$ , you can start by finding the measures of the triangle's interior angles. Knowing that a straight line measures $180$ °, you can subtract the given values from $180$ ° to find the measures of the respective supplementary interior angles. That would give you $59$ ° $(180-121)$ and $36$ ° $(180-144)$ .

Now, knowing that the measure of all the interior angles of a triangle is also $180$ °, you can add the two interior angles you know $(59+36)$ and subtract those from $180$ °. Doing so would give you the measure of the missing third angle, which is $85$ °.

Finally, because angle $n$ is the supplementary angle of the missing angle from the previous step, simply subtract that angle's measure from $180$ ° to find $n$ °, which is $180-85$ or $95$ °.

5 0

4 years ago

What is the sum of the ten thousand digit and the million's digit of 1,234,567,890

zloy xaker [14]

Answer: The ten thousand digit is 6. And the millions digit is 4. So the answer is 10.

7 0

2 years ago