Question

A coin is tossed 100 times.

(a) The difference "number of heads − number of tails" is like the sum of 100 draws from one of the following boxes. Which one? (Input should be one of i, ii, iii, iv, v)

(b) Find the expected value for the difference. (Input a number)

(c) Find the standard error for the difference. (Round and input an integer)

Answer 1

The difference "number of heads - number of tails" is like the sum of 100 draws from box (ii). The expected value for the difference is 0. The standard error for the difference is 2.

Step-by-step explanation:

(a) The difference "number of heads - number of tails" is like the sum of 100 draws from box (ii). (b) The expected value for the difference is 0, since the coin is fair and has an equal chance of landing on heads or tails. (c) The standard error for the difference is 2, since the standard deviation for the number of heads is 4 and the sample size is 100.

Answer 2

The difference "number of heads - number of tails" for 100 coin tosses can be represented by a box with outcomes of +1 and -1, with the expected value being 0 and the standard error being 5.

Step-by-step explanation:

The difference "number of heads − number of tails" is akin to the sum of 100 independent draws in which each draw gives +1 for a head and -1 for a tail. Since a fair coin has an equal chance of landing on heads or tails, the draws represent a binomial distribution that can be simplified to a normal distribution given the large number of tosses. Therefore, it might be represented by one of the possible boxes (i, ii, iii, iv, v) which would be a box with equally likely outcomes of +1 or -1.

The expected value for the difference in a fair coin toss scenario is 0 because the chance of landing on heads is equal to that of tails, for a fair coin.

To find the standard error for the difference, you would use the formula for the standard deviation of a binomial distribution, which is √(np(1-p)). With a fair coin, p = 0.5, so for 100 coin tosses (n = 100), the standard error is √(100*0.5*0.5) = 5. Therefore, the integer value for standard error is 5.