Consider a binomial experiment with n = 20 and p = .70. if you calculate the binomial probabilities manually, make sure to carry at least 4 decimal digits in your calculations. compute f(12) (to 4 decimals). 0.1143 compute f(16) (to 4 decimals). 0.1304 compute p(x 16) (to 4 decimals). 0.2375 compute p(x 15) (to 4 decimals). 0.7624 compute e(x). 14

Here are the results for the first 2 parts.

Step-by-step explanation:

f(x)   =    nCr p^r q^(n-r)

So f(12) = 20C12 (0.70^12 q^(0.30)^(20-12)

=  20C8 0.7^12 0.30^8

= 0.1144 .

f(16)  =  0.1304.

Step-by-step explanation:

The question is incomplete. p(x 16) is actually ; p(x 15) is actually and e(x) is

Wherever a random variable X can be modeled as a binomial random variable we write :

X ~ Bi (n,p)

Where ''n'' is the number of Bernoulli experiments taking place (whose variable is called binomial random variable).

And where ''p'' is the success probability.

In a Bernoulli experiment we define which event will be a ''success''

In order to calculate the probabilities for the variable X we can use the following equation :

Where '''' is the probability of the variable X to assume the value x.

Where '''' is the combinatorial number define as :

In our question

X ~ Bi (20,0.70)

Now let's calculate the probabilities :

(I)

⇒

(II)

(III)

(IV)

(V)

(VI)

Using (I), (III), (IV), (V) and (VI) in (II) :

Now :  

Finally,

μ (X)

is the mean of the variable X

In this case, X is a binomial random variable and its mean can be calculated as

In the question :