Jeans are on sale for 80% of the original price of $60. What is the sale price? A.$12 B.$24 C.$36 D.$48

Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations. If required

Mila [183]

Answer:

$\begin{tabular}{c|ccccc}{$x$&10&12&16&17&20&z&-1.397&-0.839&0.2795&0.559&1.397&\end{tabular}$

Step-by-step explanation:

z-score is denoted by:

$z=\dfrac{x-\mu}{\sigma}$

here,

$\mu$ : mean

$\sigma$ : standard deviation (or the square root of the variance)

so first we need to find the means of our sample:

$\mu=\dfrac{10+20+12+17+16}{5}\\\mu = 15\\$

Now to find the standard deviation we first need to find the variance of the sample. The variance is the sum of the squares of the differences of each value from the mean.

$\sigma^2 = \dfrac{(10-15)^2+(20-15)^2+(12-15)^2+(17-15)^2+(16-15)^2}{5}\\\sigma^2 = 12.8$

the standard derviation is simply the square root of the variance!

$\sigma = \sqrt{\sigma^2} \\\sigma = \sqrt{12.8} \\\sigma = 3.5778$

Now that we all the values for our z-score formula. we can plug it in!

$z=\dfrac{x-\mu}{\sigma}$

$z=\dfrac{x-15}{3.5778}$

Finally we'll use each value in place of x from our sample into the formula to find the z-score of each value.

$z=\dfrac{10-15}{3.5778} = -1.397$

$z=\dfrac{20-15}{3.5778} = 1.397$

$z=\dfrac{12-15}{3.5778} = -0.839$

$z=\dfrac{17-15}{3.5778} = 0.559$

$z=\dfrac{16-15}{3.5778} = 0.2795$

We can even display the z-scores in a table: (the x-values are in ascending order)

$\begin{tabular}{c|ccccc}{$x$&10&12&16&17&20&z&-1.397&-0.839&0.2795&0.559&1.397&\end{tabular}$

5 0

3 years ago

What is the greatest common factor of 8 and 18?

SCORPION-xisa [38]

Answer: 2

Step-by-step explanation: To find the greatest common factor or GCF of 8 and 18, we begin by finding all of the factors of each number.

To find the factors of 8, we know that 8 ÷ 1 is 8 so 1 and 8 are factors.

8 ÷ 2 is 4 so 2 and 4 are factors.

However, if we continue to divide 8 by 3, 4, 5, and so on, we won't find any new factors. So the factors of 8 are 1, 2, 4, and 8.

Now let's find the factors of 18.

18 ÷ 1 is 18 so 1 and 18 are factors.

18 ÷ 2 is 9 so 2 and 9 are factors.

18 ÷ 3 is 6 so 3 and 6 are factors.

However, if we continue to divide by 4, 5, 6, and so on, we won't find any new factors. So the factors of 18 are 1, 2, 3, 6, 9, and 18.

Now that we have our list of factors, to find the greatest common factor, we simply find the largest number that is shared by the two lists.

Notice that our lists share a 1 but the largest number they share is a 2.

So the greatest common factor or gcf of 8 and 18 is 2.

I have also shown my work on the whiteboard.

4 0

2 years ago

Find the simplified product where x>=0

irinina [24]

Answer:

The last one

Step-by-step explanation:

in the second part, x2 could to pull out as x

6 0

3 years ago

Read 2 more answers

We're testing the hypothesis that the average boy walks at 18 months of age (H0: p = 18). We assume that the ages at which boys

marusya05 [52]

Answer:

II. This finding is significant for a two-tailed test at .01.

III. This finding is significant for a one-tailed test at .01.

d. II and III only

Step-by-step explanation:

1) Data given and notation

$\bar X=19.2$ represent the battery life sample mean

$\sigma=2.5$ represent the population standard deviation

$n=25$ sample size

$\mu_o =18$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean battery life is equal to 18 or not for parta I and II:

Null hypothesis: $\mu = 18$

Alternative hypothesis: $\mu \neq 18$

And for part III we have a one tailed test with the following hypothesis:

Null hypothesis: $\mu \leq 18$

Alternative hypothesis: $\mu > 18$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{19.2-18}{\frac{2.5}{\sqrt{25}}}=2.4$