Statistics Probability 

Some questions ask for graphs. These will be supplied shortly.

1. a) Discrete b) continuous c) continuous d) discrete
2. The possibilities are:
(m,m), (m,f), (f,m), (f,f)
where each possiblity has probability 0.25. ( (m,f) means the first child is male, the second is female etc )
3. a)
# girls | 0     |  1   |  2
prob    | 0.25 | 0.5 | 0.25
b) It looks like this (sketch):

0.5       |     __
0.25    |__|    |__
0           |__.____.|_

The first "." is at 1, the second at 2. The height of the first line is at 0.25, the second is at 0.5 and the third at 0.25.

4. a) The z-score is -1
b) Yes, the z-score is 3.333  which is large. So this event is unlikely if  gestation periods are indeed normal distributed.

5. About 26% of women will have a shoe size of 6 or smaller.

6. About 87% of women will have a shoe size in this range.

7. a) 5% b) 29% c) 9.6%

8. a) 42% b) 48% c) 495

9. 19%

10. 40.5% b) 71.5 pounds c) roughly $2\cdot 10^{-9}$, which is very small.

11. No

12.  Roughly 67.5 inches

13. a) 66.7 b) 63.3 c) 3.4 d) Its larger, for normal distributions the interquartile range is approximately 1.35 times the standard deviation.

14. The only information given is about the distribution of the height of 6 year old girls. We are not able to say anything about the distribution of the height of 5 year old boys. The way to continue is to suppose the exercise has a typo and assume that it was really talking about the heights of 5 year old boys.
a) 60-th percentile (after rounding)
b) 71 inches

15. roughly 312 pounds.