Answer: P(22 ≤ x ≤ 29) = 0.703
Step-by-step explanation:
Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = output of the machine in ounces per cup.
µ = mean output
σ = standard deviation
From the information given,
µ = 27
σ = 3
The probability of filling a cup between 22 and 29 ounces is expressed as
P(22 ≤ x ≤ 29)
For x = 22,
z = (22 - 27)/3 = - 1.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.047
For x = 29,
z = (29 - 27)/3 = 0.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.75
Therefore,
P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703
9514 1404 393
Answer:
140°
Step-by-step explanation:
The value of the exterior angle (x°) is the sum of the other two angles shown. These are known as "remote interior angles."
x° = 64° +76°
x° = 140°
_____
<em>Additional comment</em>
This relationship derives from the fact that the exterior angle and the adjacent interior angle have a sum of 180° (they are a linear pair). We also know that the adjacent interior angle and the other two given angles have a sum of 180°.
If we call the unknown interior angle U, these relations are ...
64 + 76 + U = 180 . . . . sum of angles in a triangle
x + U = 180 . . . . . . . . . . sum of angles in a linear pair
Comparing these two equations, we see that ...
64 + 76 = x
Given:
Do you earn over $50,000 per year?
Male Female Total
Income over 50,000 475 375 850
Income below 50,000 75 75 150
Total 550 450 1,000
Yes, "being female" and "earning over 50,000" are independent events. Independents events are events that happen where the probability of one event happening is not affected by the happening of the other event.
In this case, regardless if you are male or female, you can earn over 50,000.
Also if you are female, you either earn under or over 50,000