Answer:
16% probability that the facility needs to recalibrate their machines.
Step-by-step explanation:
We have to use the Empirical Rule to solve this problem.
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
What is the probability that the facility needs to recalibrate their machines?
They will have to recalibrate if the number of defects is more than one standard deviation above the mean.
We know that by the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% is more than 1 standard deviation from the mean. Since the normal distribution is symmetric, of those 32%, 16% are more than one standard deviation below the mean, and 16% are more than one standard deviation above the mean.
So there is a 16% probability that the facility needs to recalibrate their machines.
Answer:
Suppose there are 1,000 candies in a jar. There are 50 children in a room. If i want to share 1000 candies among all the children. How can i divide 1,000 candies equally in 50 children.
Step-by-step explanation:
Create a story line(word problem) means to create a fake or real story by translating an algebraic expression in english.
We can create a story by the given 1,000/r:
Suppose there are 1,000 candies in a jar. There are 50 children in a room. If i want to share 1000 candies among all the children. How can i divide 1,000 candies equally in 50 children.
Here r = 50....
Solving this problem actually requires us the use of the
distance formula of point to a line.
The formula is:
distance = | a x + b y + c | / sqrt (a^2 + b^2)
So we are given the equation:
y = 2 x + 4
rewriting:
<span>y – 2 x – 4 = 0 -->
a = -2, b = 1, c = -4</span>
We are also given the points:
(-4, 11) = (x, y)
Using the distance formula at points (x, y):
distance = | -2 * -4 + 1 * 11 + -4 | / sqrt [(- 2)^2 +
(1)^2]
distance = 15 / sqrt (5)
distance = 6.7
<span>So the tree is about 6.7 ft away from the zip line.</span>
Answer:
7.5
Step-by-step explanation:
106% of $x = $7.95
In other words,
![\[\frac{106}{100}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B106%7D%7B100%7D%5C%5D)
of $x = 7.95
Multiplying both sides of the equation by ![\[\frac{100}{106}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B100%7D%7B106%7D%5C%5D)
![\[\frac{106}{100} * \frac{100}{106}\]](https://tex.z-dn.net/?f=%5C%5B%5Cfrac%7B106%7D%7B100%7D%20%2A%20%5Cfrac%7B100%7D%7B106%7D%5C%5D)
of x = 7.95 * ![[\frac{100}{106}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B100%7D%7B106%7D%5D)
=> x = ![[\frac{750}{100}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B750%7D%7B100%7D%5D)
=> x = ![[\frac{7.50}{1}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B7.50%7D%7B1%7D%5D)
=> x = 7.5
Validation: 106% of 7.5 = 7.95
