Dennis and Eduardo are studying transformations using triangles. A ABC and A DEF are both plotted on a coordinate plane

A simple random sample of size nequals81 is obtained from a population with mu equals 83 and sigma equals 27. (a) Describe the

Ivanshal [37]

Answer:

a) $\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

b) $z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

c) $z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

d) $z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

Step-by-step explanation:

For this case we know the following propoertis for the random variable X

$\mu = 83, \sigma = 27$

We select a sample size of n = 81

Part a

Since the sample size is large enough we can use the central limit distribution and the distribution for the sampel mean on this case would be:

$\bar X \sim N (\mu, \frac{\sigma}{\sqrt{n}})$

With:

$\mu_{\bar X}= 83$

$\sigma_{\bar X}=\frac{27}{\sqrt{81}}= 3$

Part b

We want this probability:

$P(\bar X>89)$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 89 we got:

$z= \frac{89-83}{\frac{27}{\sqrt{81}}}= 2$

$P(Z>2) = 1-P(Z$

Part c

$P(\bar X$

We can use the z score formula given by:

$z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}$

And if we find the z score for 75.65 we got:

$z= \frac{75.65-83}{\frac{27}{\sqrt{81}}}= -2.45$

$P(Z$

Part d

We want this probability:

$P(79.4 < \bar X < 89.3)$

We find the z scores:

$z= \frac{89.3-83}{\frac{27}{\sqrt{81}}}= 2.1$

$z= \frac{79.4-83}{\frac{27}{\sqrt{81}}}= -1.2$

$P(-1.2$

8 0

3 years ago

Mike took clothes to the cleaners three times last month. First, brought 4 shirts and of slacks and paid $11.45. Then brought

GenaCL600 [577]

Complete Question:

Mike took clothes to the cleaners three times last month. First, brought 4 shirts and 1 pair of slacks and paid $11.45. Then brought 7 shirts, 2 pairs of slacks, and 2 sports and paid $35.39. Finally, brought 5 shirts and 2 sports and paid $21.43 . How much was charged for each shirt, each pair of slacks, and each sports coat?

Answer:

The charges

For each Shirt = $1.49

For each pair of slacks = $5.49

For each sports coat = $6.99

Step-by-step explanation:

Let Shirt = a

Let pair of slacks = b

Let sports coat = c

First, brought 4 shirts and 1 pair of slacks and paid $11.45

= 4a + b = 11.45 ..........Equation 1

b = 11.45 - 4a

Then brought 7 shirts, 2 pairs of slacks, and 2 sports and paid $35.39

= 7a + 2b + 2c = 35.39.........Equation 2

5 shirts and 2 sports and paid $21.43

5a + 2c = 21.43............Equation 3

Hence:

4a + b = 11.45 ..........Equation 1

7a + 2b + 2c = 35.39.........Equation 2

Using elimination method

Multiply Equation 2 by the coefficient of b = 1 in Equation 1

Multiply Equation 1 by the coefficient of b = 2 in Equation 2

8a + 2b = 22.9 .......Equation 4

7a + 2b + 2c = 35.39.........Equation 2

Subtracting Equation 2 from Equation 4

= a - 2c = -12.49 ........Equation 5

a = -12.49 + 2c

Subtituting -12.49 + 2c for a in Equation 3

5a + 2c = 21.43............Equation 3

5(-12.49 + 2c) + 2c = 21.43

= -62.45 + 10c + 2c = 21.43

Collecting like terms

10c + 2c = 21.43 + 62.45

12c = 83.88

c = 83.88/12

c = 6.99

5a + 2c = 21.43............Equation 3

Substituting 6.99 for c in Equation 3

5a + 2(6.99) = 21.43

5a + 13.98 = 21.43

5a = 21.43 - 13.98

5a = 7.45

a = 7.45/5

a = 1.49

4a + b = 11.45 ..........Equation 1

Substituting 1.49 for a in Equation 1

4(1.49) + b = 11.45

b = 11.45 - 4(1.49)

b = 11.45 - 5.96

b = 5.49

Therefore, since the charges

For each shirt = a

The charges for each Shirt = $1.49

For each pair of slacks = b

The charges for each pair of slacks = $5.49

For each sports coat = c

The charges for each sports coat = $6.99

3 0

2 years ago

12.12.12.12 +7(3.3.3.3+3)<br> What the answer

Black_prince [1.1K]

Answer:

23.253528

Your welcome

4 0

2 years ago

Will give brainliest

Marianna [84]

A. Commutative Property

"The commutative property states that the order in which two numbers are added or multiplied does not affect the sum or product." ~ ck12.org

May I have brainliest please? :)

3 0

3 years ago

Aria had $20 in her savings account. She went through $10. What is the balance of your savings account now?

Elena L [17]

Subtract 20 and 10. To get your answer

3 0

3 years ago