Answer: A) .1587
Step-by-step explanation:
Given : The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.30 ounces and a standard deviation of 0.20 ounce.
i.e. 
and 
Let x denotes the amount of soda in any can.
Every can that has more than 12.50 ounces of soda poured into it must go through a special cleaning process before it can be sold.
Then, the probability that a randomly selected can will need to go through the mentioned process = probability that a randomly selected can has more than 12.50 ounces of soda poured into it =
![P(x>12.50)=1-P(x\leq12.50)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{12.50-12.30}{0.20})\\\\=1-P(z\leq1)\ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.8413\ \ \ [\text{By z-table}]\\\\=0.1587](https://tex.z-dn.net/?f=P%28x%3E12.50%29%3D1-P%28x%5Cleq12.50%29%5C%5C%5C%5C%3D1-P%28%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5Cleq%5Cdfrac%7B12.50-12.30%7D%7B0.20%7D%29%5C%5C%5C%5C%3D1-P%28z%5Cleq1%29%5C%20%5C%20%5B%5Cbecause%20z%3D%5Cdfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%5D%5C%5C%5C%5C%3D1-0.8413%5C%20%5C%20%5C%20%5B%5Ctext%7BBy%20z-table%7D%5D%5C%5C%5C%5C%3D0.1587)
Hence, the required probability= A) 0.1587
Answer:
Before going to the first store he had $ 112.
Step-by-step explanation:
Before going to the first store Mr. Chin had all his money, which we will call by "x". After the first store he had:
y = x/2 - 14
He then went to a second store and he spent all his money in a way that:
y/3 - 14 = 0
Because after that store he had no money left. So we can use the second equation to solve for y and then use that value to solve for x, that is the amount of money he had before going to the first store. We have:
y/3 = 14
y = 14*3 = 42
From the first equation:
42 = x/2 - 14
x/2 - 14 = 42
x/2 = 42 + 14
x/2 = 56
x = 112
Before going to the first store he had $ 112.
Using statistical concepts, we have that:
- a. The range is 6 days, and the interpretation is: B. The number of days separating the fewest and most sick days taken is equal to the range.
- b. The standard deviation is of 2.2, which means that the average spread about the mean is of 2.2 units.
<h3>Range and standard deviation:</h3>
- The range of a data-set is given by the difference <u>between the highest value and the lowest value in the data-set</u>.
- The standard deviation of a data-set is given by the <u>square root of the sum of the difference squared of each observation and the mean, divided by the number of observations</u>.
Item a:
- The lowest value is of 0.
- The highest value is of 6.
Hence:
The range is 6 days, and the interpretation is: B. The number of days separating the fewest and most sick days taken is equal to the range.
Item b:
The mean is:
Hence, the standard deviation is:
The standard deviation is of 2.2, which means that the average spread about the mean is of 2.2 units.
You can learn more about range and standard deviation at brainly.com/question/11729451
1:3 or 1 to 3. First write 12:36 and then simplify which gives you 1:3 or 1 to 3
