Answer:
x = 1/2 or 2
Step-by-step explanation:
You can factor this as ...
2x^2 -4x -x +2 = 0 . . . rewrite the middle term to enable factoring
2x(x -2) -1(x -2) = 0 . . . . factor by grouping
(2x -1)(x -2) = 0 . . . . factor out (x -2)
x = 1/2, 2 . . . . . . values of x that make the factors zero
Answer:
a) 0.0287 = 2.87% probability that three non-defective components in a batch of seven components.
b) 0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.
Step-by-step explanation:
A sequence of Bernoulli trials composes the binomial distribution.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
The probability that a selected component is non-defective is 0.8
This means that
a) Three non-defective components in a batch of seven components.
This is P(X = 3) when n = 7. So
0.0287 = 2.87% probability that three non-defective components in a batch of seven components.
b) 8 non-defective components are drawn before the first defective component is chosen.
Now the order is important, so the we just multiply the probabilities.
8 non-defective, each with probability 0.8, and then a defective, with probability 0.2. So
0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.
Answer:
A. We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.
B. Null hypothesis:
Alternative hypothesis:
C.
D.
E. Fail to the reject the null hypothesis
F. So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of inaccurate orders is not significantly different from 0.1.
Step-by-step explanation:
Data given and notation
n=362 represent the random sample taken
X=33 represent the number of orders not accurate
estimated proportion of orders not accurate
is the value that we want to test
represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
A: Write the claim as a mathematical statement involving the population proportion p
We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.
B: State the null (H0) and alternative (H1) hypotheses
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statistic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
C: Find the test statistic
Since we have all the info required we can replace in formula (1) like this:
D: Find the critical value(s)
Since is a bilateral test we have two critical values. We need to look on the normal standard distribution a quantile that accumulates 0.025 of the area on each tail. And for this case we have:
P value
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
E: Would you Reject or Fail to Reject the null (H0) hypothesis.
Fail to the reject the null hypothesis
F: Write the conclusion of the test.
So the p value obtained was a very high value and using the significance level given we have
so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of inaccurate orders is not significantly different from 0.1.