How do you express 4 feet 9 inches into height in feet only using a mixed number?

1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)

Natalija [7]

Answer:

0.6826 = 68.26% probability that you have values in this interval.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

X~N(8, 1.5)

This means that $\mu = 8, \sigma = 1.5$

What is the probability that you have values between (6.5, 9.5)?

This is the p-value of Z when X = 9.5 subtracted by the p-value of Z when X = 6.5. So

X = 9.5

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

$Z = \frac{9.5 - 8}{1.5}$

$Z = 1$

$Z = 1$ has a p-value of 0.8413.

X = 6.5

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

$Z = \frac{6.5 - 8}{1.5}$

$Z = -1$

$Z = -1$ has a p-value of 0.1587

0.8413 - 0.1587 = 0.6826

0.6826 = 68.26% probability that you have values in this interval.

7 0

3 years ago

A certain brand of dinnerware set comes in three colors: red, white, and blue. Twenty percent of customers order the red set, 45

denis23 [38]

Answer:

a) 0.20

b) 0.45

c) 0.65

d) Yes

e) Yes

f) Z = X + Y (except when X = 1 and Y = 1)

This is because the successes of X and Y are mutually exclusive events but their failures aren't. X and Y cannot both be 1.

Step-by-step explanation:

Probability of a red set = 20% = 0.20

Probability of a white set = 45% = 0.45

Probability of a blue set = 35% = 0.35

Probability of the single set being a red or white set = 20% + 45% = 65% = 0.65

P(X=1) = 0.20, P(X=0) = 1 - 0.2 = 0.80

P(Y=1) = 0.45, P(Y=0) = 1 - 0.45 = 0.55

P(Z=1) = 0.65, P(Z=0) = 1 - 0.65 = 0.35

a) pX = P(X=1) = 0.20

b) pY = P(Y=1) = 0.45

c) pZ = P(Z=1) = 0.65

d) Since only one order is being considered at a time, it isn't possible to order red & white set in a single set, hence, both X and Y cannot both be successes (equal to 1) at the same time. But they can both be failures (both equal to 0) if a blue set is ordered. The successes of X and Y are mutually exclusive events but their failures aren't

e) Is pZ = pX + pY

pX = 0.2, pY = 0.45, pZ = 0.65

Hence, this statement is correct!

f) Z = X + Y

Let's check all the probabilities

when X = 1 and Y = 1, Z = 1

1 ≠ 1 + 1

when X = 0 and Y = 1, Z = 1

1 = 0 + 1

when X = 1 and Y = 0, Z = 1

1 = 1 + 0

when X = 0 and Y = 0, Z = 0

0 = 0 + 0

Hence, Z = X + Y (except when X = 1 and Y = 1)

This is because the success of X and Y are mutually exclusive events but their failures aren't.

8 0

3 years ago

What is the solution of <img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B4%7D%20%3D%20%5Cfrac%7Bx%2B8%7D%7B3%7D" id="TexFo

Lina20 [59]

Answer:

x = -26

Step-by-step explanation:

Multiply both sides by the lowest common multiple of 4 and 3, which is 12.

3(x+2) = 4(x+8)

3x + 6 = 4x + 32 --- distribute the 4 and 3

6 = x + 32 --- subtract 3x from both sides

-26 = x --- subtract 32 from both sides

x = -26

6 0

3 years ago

What is X in this situation? I'm thinking that you could get X, via vertical angles, but I'm not too sure.

attashe74 [19]

Use alternate interior angles.
The angle to the left of x is 32
The angle to the right of x is 68
Since the three angles(32, x, and 68) form a straight line, they are supplementary.
32+x+68=180
100+x=180 x=80

4 0

3 years ago

What is y+2= (-3) (x-4)

TEA [102]

Y=-3x+10 is your awnser

3 0

3 years ago

Read 2 more answers