Because we are given that the target was hit, we only need to look at those outcomes. P (the person
who hit the target was Laura|the target was hit)- μX–Y = μX – μY = 3 –5 = –2.
Since X and Y are independent, we have . Note that the variances
add even though we are subtracting one random variable from another.
I is not true. This is an approximation based on the 68-95-99.7 rule . The actual value proportion
within two standard deviations of the mean, to 4 decimal places, is 0.9545.
II is true. This is a property of the normal curve.
III is true. This is because the bell shape of the normal curve means that there is more area under the
curve for a given interval length for intervals closer to the center.
- (a) No, the events are not independent. The probability of B changes depending on what happens with
A · Because there are 12 face cards, if the first card drawn is a face card, then P (B) = 11/51. If
the first card is not a face card, then P (B) = 12/51. Because the probability of B is affected by the
outcome of A, A and B are not independent.
(b) P (A) = 12/52 = 3/13. P (A| C) = 3/13 (3 of the 13 diamonds are face cards). Because these are
the same, the events “draw a face card on the first draw” and “the first card drawn is a diamond”
are independent. - The area to the right of x is 0.6, so the area to the left is 0.4. From the table of Standard Normal
Probabilities, A = 0.4 z (^) x = – 0.25. Also
So,
60% of the area is to the right of 687.5. The calculator answer is given by invNorm(0.4,700,50)