Question

Suppose you toss a fair coin​ 10,000 times. Should you expect to get exactly 5000​ heads? Why or why​ not? What does the law of large numbers tell you about the results you are likely to​ get? Choose the correct answer below.

1)Should you expect to get exactly 5000​ heads? Why or why​ not?

A)You​ shouldn't expect to get exactly 5000​ heads, because you cannot predict precisely how many heads will occur.

B.You​ shouldn't expect to get exactly 5000​ heads, because it is not easy to count precisely the number of heads that occurred.

C.You should expect to get exactly 5000​ heads, because for a fair​ coin, the proportion of heads is exactly​ 50%.

D.You should expect to get exactly 5000​ heads, because the proportion of heads should be​ 50% for such a large number of tosses.

2) What does the law of large numbers tell you about the results you are likely to​ get?

A. The proportion of heads should approach 0.5 as the number of tosses decreases.

B.The proportion of heads should approach 0.5 as the number of tosses approaches an exact number.

C.The proportion of heads should not approach 0.5 as the number of tosses increases.

D.The proportion of heads should approach 0.5 as the number of tosses increases.

Answer 1

(1)

Correct option:

(A) You shouldn't expect to get exactly 5000 heads, because you cannot predict precisely how many heads will occur.

Explanation: It is not possible to exactly calculate population parameter from sample statistic.We can only make estimate the parameter.

(2)

Correct option:

(D) The proportion of heads should approach 0.5 as the number of tosses increases.

Explanation:By law of large numbers, as the sample size increases the sample statistics will approach population parameter.