a studio needs 3 actors On a fair coin each side has an equa

On a fair coin, each side has an equal probability of coming up. When a fair coin is flipped n times, the most likely outcome (the mean) is that each side will come up n/2 times, with a standard deviation of sigma =square root n / 2 Megan flips a coin 50 times. She will conclude that the coin 2 is unfair if the number of times either side is flipped is outside 1.5 standard deviations of the mean. Show your calculations to complete the statement below. The coin will be considered fair if her results show \"heads\" at least times and no more than times.

Solution

As u = n/2
sigma = sqrt(n)/2

Then the lower and upper bounds of the acceptable region are

u - 1.5*sigma < x < u - 1.5*sigma

n/2 - 1.5*(sqrt(n)/2) < x < n/2 + 1.5*(sqrt(n)/2)

n/2 - 0.75*sqrt(n) < x < n/2 + 0.75*sqrt(n)

Thus,

FIRST BLANK: n/2 - 0.75*sqrt(n)
SECOND BLANK: n/2 + 0.75*sqrt(n) [ANSWERS]