What is expected value for the number of heads

Question

Discussion:

1. The figure below shows the probability histogram for the total number of spots when a die is rolled eight times. The shaded area represents the chance that the total will be between__ _ and ___ (inclusive).

2. A coin is tossed 100 times. True or false, and explain:

(a) The expected value for the number of heads is 50.

(b) The expected value for the number of heads is 50, give or take 5 or so.

(c) The number of heads will be 50.

(d) The number of heads will be around 50, give or take 5 or so.

3. The below data contains measurements made on men involved in a physical fitness course at N.C. State University. The variables are age (years), weight (kg), oxygen intake rate (ml per kg body weight per minute), time to run 1.5 miles (minutes), heart rate while resting, heart rate while running (same time oxygen rate measured), and maximum heart rate recorded while running.

a. For the variables age and weight calculate their means and standard deviations

b. Determine whether these variables are approximately normally distributed.

c. For the variables age and weight calculate a 95% confidence interval for the mean.

d. Define a new variable that classifies individuals as ‘old' or ‘young' according to whether they are below or above 43 years old. Then calculate means, standard error and a 95% confidence interval for the mean time to run 1.5 miles for both the young and the old individuals. Do they seem different to you?

e. Write a brief report of your answers.

age	weight	oxygen	runtime	rstpulse	runpulse	maxpulse
44	89.47	44.609	11.37	62	178	182
40	75.07	45.313	10.07	62	185	185
44	85.84	54.297	8.65	45	156	168
42	68.15	59.571	8.17	40	166	172
38	89.02	49.874	9.22	55	178	180
47	77.45	44.811	11.63	58	176	176
40	75.98	45.681	11.95	70	176	180
43	81.19	49.091	10.85	64	162	170
44	81.42	39.442	13.08	63	174	176
38	81.87	60.055	8.63	48	170	186
44	73.03	50.541	10.13	45	168	168
45	87.66	37.388	14.03	56	186	192
45	66.45	44.754	11.12	51	176	176
47	79.15	47.273	10.6	47	162	164
54	83.12	51.855	10.33	50	166	170
49	81.42	49.156	8.95	44	180	185
51	69.63	40.836	10.95	57	168	172
51	77.91	46.672	10	48	162	168
48	91.63	46.774	10.25	48	162	164
49	73.37	50.388	10.08	67	168	168
57	73.37	39.407	12.63	58	174	176
54	79.38	46.08	11.17	62	156	165
52	76.32	45.441	9.63	48	164	166
50	70.87	54.625	8.92	48	146	155
51	67.25	45.118	11.08	48	172	172
54	91.63	39.203	12.88	44	168	172
51	73.71	45.79	10.47	59	186	188
57	59.08	50.545	9.93	49	148	155
49	76.32	48.673	9.4	56	186	188
48	61.24	47.92	11.5	52	170	176
52	82.78	47.467	10.5	53	170	172