Expected Frequencies of Heads

To find the expected frequencies of heads when 6 coins are tossed 512 times, we need to use the probability formula.

The probability of getting a head when tossing a coin is 1/2 or 0.5.

Therefore, the expected frequency of heads for one coin toss is:

Expected frequency of heads = Probability of getting heads x Number of coin tosses

Expected frequency of heads = 0.5 x 512

Expected frequency of heads = 256

Since we are tossing 6 coins, the expected frequency of heads for all 6 coins is:

Expected frequency of heads = 6 x 256

Expected frequency of heads = 1536

Therefore, the expected frequencies of heads when 6 coins are tossed 512 times is 1536.

Mean and Standard Deviation of Number of Heads

To find the mean and standard deviation of the number of heads, we need to use the binomial distribution formula.

The binomial distribution formula for the mean is:

Mean = n x p

Where n is the number of trials (in this case, 512) and p is the probability of success (in this case, 0.5).

Therefore, the mean of the number of heads is:

Mean = 512 x 0.5

Mean = 256

The binomial distribution formula for the standard deviation is:

Standard deviation = √(n x p x q)

Where q is the probability of failure (in this case, 0.5).

Therefore, the standard deviation of the number of heads is:

Standard deviation = √(512 x 0.5 x 0.5)

Standard deviation = √128

Standard deviation = 11.31 (rounded to two decimal places)

Therefore, the mean of the number of heads is 256 and the standard deviation is 11.31 when 6 coins are tossed 512 times.