answer is 72
ella ran 3times as many and vera
24 x3=72 miles more
Answers:
- (a) Independent
- (b) Dependent
- (c) Dependent
- (d) Independent
========================================================
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.
------------------------
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.
------------------------
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.
------------------------
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.
Step-by-step explanation:
Margin of error = critical value × standard deviation
We aren't given the critical value or any information to calculate it, so we need to make some assumptions. Assuming the data set is large enough to be approximated as normal, and that the confidence level is 95%, then the critical value is 1.96.
ME = 1.96 × 9.5
ME = 18.62
You may choose to round 1.96 to 2, in which case the margin of error is:
ME = 2 × 9.5
ME = 19
