Twenty students are asked to select an integer between 1

Solution :

Step 1 of 2:

Let n denotes 20 students asked to select an integer between 1 and 10.

Here n=20

p=and

q=1-p

q=1-0.3

q=0.7

Our goal is:

a). We need to find the probability that 8 or more will select 4,5 or 6.

b). We observed 8 students who selected 4,5, or 6.We need to conclude our answer to part (a).

a).

If the students make their choices independently and each is as likely to pick one integer as any other, then we have to find the probability that 8 or more will select 4,5 or 6.

We know that n=20, p=0.3 and q=0.7.

The formula for the binomial probability is

P(X=a)=

Then the probability that 8 or more is

P(X8)= P(X=8)+P(X=9)+P(X=10)+,...,+P(X=20)

P(X8)=

We know that n=20, p=0.30.

Where, P(X=8),P(X=9),P(X=10),...,P(X=20) is obtained from Excel by using the function “=Binomdist(x,n,p,false)”

Then the table is given below.

P(X8)= P(X=8)+P(X=9)+P(X=10)+,...,+P(X=20)

P(X8)= 0.11439+0.065369+0.030817,...,3.48678E-11

P(X8)= 0.2277

Therefore the probability that 8 or more will select 4,5 or 6 is 0.2277.