Answer: About 0.8034 of the items will be classified as good.
Step-by-step explanation:
Let's first understand that because 13% of the items are defective, that means 87% of the items are not defective. And because the inspector incorrectly classifies the items 9% of the time, it's important to understand that that means both the defective and the not defective items may be incorrectly classified. In order to figure out what proportion will be classified as 'good,' let's set up a tree diagram:
--0.13--defective
|__0.09__ classified as 'good'
|__0.91__ classified as 'defective'
--0.87--not defective
|__0.09__ classified as 'defective'
|__0.91__classified as 'good'
This chart essentially reiterates the information in the prompt, showing that 9% of each type of item will be incorrectly classified. Now we need to find the proportion of items that will be classified as 'good.' To do this, we must multiply the proportion of items classified as 'good' by the proportion of items that are either defective or not defective for both types, like this:
(0.13 * 0.09) + (0.87 * 0.91)
this expression in words means: "13% of the items will be classified as good 9% of the time, and the other 87% of the items will be classified as good 91% of the time"
When we multiply and add these numbers together, we get 0.8034, but you should round to 2 or 3 decimal places like the prompt instructs. Hope this helped! :)
Answer:
1) The system of equations is 
and 
2) The first number is 
and the second number is 
Step-by-step explanation:
1) Let be "x" the first number and "y" the second number.
Remember that:
a- The word "times" indicates multiplication.
b- A sum is the result of an addition.
c- "Is" indicates this sign: 
Then, the sum of 5 times "x" and 4 times "y" is 75, can written as:
And "The sum of the two numbers is 18" can written as:
Therefore, the System of equations is:
2) You can use the Elimination Method to solve it:
- Multiply the second equation by -5, add the equations and then solve for "y":
- Substitute the value of "y" into any original equation and solve for "x":
Answer:
45.88%
Step-by-step explanation:
We have in this case a binomial distribution when p = 0.25, since the probability is 25%
. The formula that we will use in excel is BINOM.DIST, separated by commas we must put the value of x, n, p and also if it is true or false. We know that n equals 32.
In this case we need to know when x = 7, 8 and 9 and add this, and thus we will obtain the probability:
P (X = 7) + P (X = 8) + P (X = 9)
Excel formulas: = BINOM.DIST (7,32,0.25, FALSE) + BINOM.DIST (8,32,0.25, FALSE) + BINOM.DIST (9,32,0.25, FALSE)
P = 0.1546 + 0.1610 + 0.1431
P = 0.4588
Probability that steve agrees with the company's claim 45.88%
