How many different triangles can be constructed using angle measurements 81°,52°,47°?
1 answer:
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Answer:
a) 0.21% probability that there are no bad peaches in the peach cobbler.
b) 99.79% probability of having at least 1 bad peach in the peach cobbler
c) 7.91% probability of having exactly 2 bad peaches in the peach cobbler.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The order in which the peaches are chosen is not important. So the combinations formula is used to solve this question.
Combinations formula:
is the number of different combinations of x objects from a set of n elements, given by the following formula.
(a) If you make a peach cobbler of 12 peaches randomly selected from the box, what is the probability that there are no bad peaches in the peach cobbler?
Desired outcomes:
12 good peaches, from a set of 12. So
Total outcomes:
12 peaches, from a set of 15. So
Probability:
0.21% probability that there are no bad peaches in the peach cobbler.
(b) What is the probability of having at least 1 bad peach in the peach cobbler?
Either there are no bad peaches, or these is at least 1. The sum of the probabilities of these events is 100%. So
p + 0.21 = 100
p = 99.79
99.79% probability of having at least 1 bad peach in the peach cobbler
(c) What is the probability of having exactly 2 bad peaches in the peach cob- bler?
Desired outcomes:
2 bad peaches, from a set of 3.
One good peach, from a set of 12.
Total outcomes:
12 peaches, from a set of 15. So
Probability:
7.91% probability of having exactly 2 bad peaches in the peach cobbler.
Answer:
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 634 at 10% of signficance.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is different from 634, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 634 at 10% of signficance.