Question

# find the mean, variance and standard deviation for the binomial distribution below. a) 10 coin flips,...

find the mean, variance and standard deviation for the binomial distribution below.

a) 10 coin flips, x- number of heads. use formula np, npq

b) 5 dice rolls, x= number of sixes. use formula np, npq

c) 10 item multiple choice quiz (a,b,c,d), x = number correct while guessing. use formula np, npq

d) would it be unusual to get a passing grade (6 or more correct) on a 10 item quiz, as described above, when guessing? use formula np, npq

a)

Here , we are given that :

n = Number of trials = Number of coins = 10

We know that :

p = Probability of heads = 0.5

q = 1 - p = 1 - 0.5 = 0.5

So,

b)

Here , we are given that :

n = Number of trials = Number of dice = 5

We know that :

p = Probability of six = 1/6

q = 1 - p = 1 - 1/6 = 5/6

So,

c)

Here , we are given that :

n = Number of trials = Number of items = 10

We know that :

p = Probability of correctly guessing = 1/4

q = 1 - p = 1 - 1/4 = 3/4

So,

d)

Any value greater than Mean + 3*Standard deviation is unusual in a data set

Mean + 3*Standard deviation = 2.5 + 3*0.968 = 5.4

So, Number of questions correctly guess below 5.4 are usual. Not more than that.

Hence, it would be unusual to get a passing grade( 6 or more) on a 10 item quiz