Answers:
- (a) Independent
- (b) Dependent
- (c) Dependent
- (d) Independent
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Explanation:
If events A and B are independent, then the two following equations must both be true
- P(A | B) = P(A)
- P(B | A) = P(B)
This is because the conditional probability P(A|B) means "P(A) when B has happened". If B were to happen, then P(A) must be the same as before. In other words, event B does not affect A, and vice versa.
For part (a), we have P(B) = 1/4 and P(B|A) = 1/4 showing that P(B|A) = P(B) is true, and therefore we can say the events are independent. We don't need the info that P(A) = 1/8.
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Unlike part (a), part (b) has the answer "dependent" because P(A) = 1/8 and P(A | B) = 1/3 differ in value. Event A starts off at probability 1/8, but then event B occurring means P(A) gets increased to 1/3. The prior knowledge about B changes the chances of A. The P(B) = 1/5 is unneeded.
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If A and B were independent, then,
P(A and B) = P(A)*P(B)
However,
P(A)*P(B) = (1/4)*(1/5) = 1/20
which is not the same as P(A and B) = 1/6. Therefore the two events are dependent.
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Refer back to part (a)
P(A) = 1/4 and P(A|B) = 1/4 are identical in value, so P(A|B) = P(A) which leads to the events being independent. Whether we know event B happened or not, it does not affect the outcome of event A. P(B) = 1/9 is unneeded.
Using the normal distribution, it is found that there is a 0.9192 = 91.92% probability that the total amount of product is less than 575 g.
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- When two normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.
In this problem, the product is composed by flakes and raisins, and we have that:

Hence, the distribution for the total amount of product has <u>mean and standard deviation</u> given by:


The probability that the total amount of product is less than 575 g is the <u>p-value of Z when X = 575</u>, hence:



has a p-value of 0.9192.
0.9192 = 91.92% probability that the total amount of product is less than 575 g.
A similar problem is given at brainly.com/question/22934264
Answer:
if its A PACK then it would be 3 dollars but this is absolutely wrong i already know it LOL