Question

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

Answer 1

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