Which statements are true regarding the expression below? Check all that apply.

A data set with a mean of 34 and a standard deviation of 2.5 is normally distributed

tresset_1 [31]

Answer:

a) $z= \frac{34-34}{2.5}= 0$

$z= \frac{39-34}{2.5}= 2$

And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %

b) $P(X$

$z= \frac{31.5-34}{2.5}= -1$

So one deviation below the mean we have: (100-68)/2 = 16%

c) $z= \frac{29-34}{2.5}= -2$

$z= \frac{36.5-34}{2.5}= 1$

For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%

Step-by-step explanation:

For this case we have a random variable with the following parameters:

$X \sim N(\mu = 34, \sigma=2.5)$

From the empirical rule we know that within one deviation from the mean we have 68% of the values, within two deviations we have 95% and within 3 deviations we have 99.7% of the data.

We want to find the following probability:

$P(34 < X$

We can find the number of deviation from the mean with the z score formula:

$z= \frac{X -\mu}{\sigma}$

And replacing we got

$z= \frac{34-34}{2.5}= 0$

$z= \frac{39-34}{2.5}= 2$

And we want the probability from 0 to two deviations above the mean and we got 95/2 = 47.5 %

For the second case:

$P(X$

$z= \frac{31.5-34}{2.5}= -1$

So one deviation below the mean we have: (100-68)/2 = 16%

For the third case:

$P(29 < X$

And replacing we got:

$z= \frac{29-34}{2.5}= -2$

$z= \frac{36.5-34}{2.5}= 1$

For this case below 2 deviation from the mean we have 2.5% and above 1 deviation from the mean we got 16% and then the percentage between -2 and 1 deviation above the mean we got: (100-16-2.5)% = 81.5%

7 0

3 years ago

4. The length of Marshall’s rectangular poster is 2 times its width. If the perimeter is 24 inches, what is the area of the post

lubasha [3.4K]

The length is 7 with a width of 5, so the area is 35

3 0

3 years ago

12 + 5x > 2 ( 8x - 6 ) - 7x<br><br>x > what number?

Aloiza [94]

12 + 5x > 2(8x - 6) - 7x

12 + 5x > 16x - 12 - 7x

5x - 16x + 7x > -12 - 12

-4x > -24 / : (-4)

x < 6

3 0

3 years ago

Read 2 more answers

Tony bought 14 pounds of rice for $6 how many dollars did he pay per pound of rice

juin [17]

Answer: 43 cents

Step-by-step explanation: divide 6.00 by 14 which gives you around .42857

then you round to the hundredths place which gives you .43

7 0

3 years ago

Read 2 more answers

Some members of the cooking club are making cakes which they will sell at a street fair for $10 apiece. It costs $10 for a booth

Alika [10]

Answer:

The cooking club sales covers the expenditure when 2 piece of cakes are sold.

Step-by-step explanation:

Given:

Selling price of each piece of cake = $10

Cost for booth at fair = $10

Ingredients for each piece of cake = $5

We need to find the number of pieces of cake sold when the sales cover the expenditures.

Solution:

Let the number of pieces be 'x'

So We can say that the point at which the sales cover the expenditures can be calculated as Selling price of each piece of cake multiplied by number of pieces will be equal to Cost for booth at fair plus Ingredients for each piece of cake multiplied number of piece of cakes.

framing in equation form we get;

$10x =10+5x$

Now Subtracting both side by '5x' using Subtraction property we get;

$10-5x=10+5x-5x\\\\5x=10$

Now Dividing both side by 5 we get;

$\frac{5x}{5}=\frac{10}{5}\\\\x=2$

Hence The cooking club sales covers the expenditure when 2 piece of cakes are sold.

7 0

3 years ago