Question

Calculate the Probability *Binomial Distribution*

Shooting Range Exercise

◦ Event {Hitting Bullseye} P(Success) = .75

1. If the event is repeated 10 times, determine:

a. Hitting Bullseye 3 times

b. Missing bullseye all 10 times

c. Hitting bullseye less than 10 times

d. Hitting Bullseye at least 5 times

e. Hitting bullseye at least 2 times

2. Calculate mean, variance and standard deviation

PLEASE TYPE ANSWER OR WRITE IN A VERY CLEAR & UNDERSTANDABLE HANDWRITING (TYPING PREFERRED) THANK YOU!!

Answer 1

Solution:- We have

X: the event of hitting Bullseye

p=Probability of success = 0.75

n= event is repeated n times =10

From above information,

X~Binomial(n=10, p=0.75) distribution

Now,pmf of X is given by

Mean And Variance of binomial distribution is

####1####

a) probability of hitting Bullseye 3 time?

----> that is, we have to find,

By using Excel command, probability can be calculated as

It gives

Therefore,

Probability of hitting Bullseye 3 time= 0.0031

b) probability of missing Bullseye all 10 times?

--->that is, we have to find

That means,

That is,

By using Excel command, above probability can be calculated as

IT gives value of

Therefore,

c) probability of hitting Bullseye less than 10 times?

--->that is,we have to find

That is,

Therefore,by using Excel command, above probability can be calculated as,

It gives value of

Therefore,

Therefore, probability of hitting Bullseye less than 10 times. = 0.9437

d) probability of hitting Bullseye atleast 5 times?

----> that is we have to find

Therefore,by using Excel command, above probability can be calculated as,

It gives value of

Therefore,

Therefore,

Probability of hitting Bullseye atleast 5 times = 0.9803

e) probability of hitting Bullseye atleast 2 times?

---->that is we have to find

Therefore,by using Excel command, above probability can be calculated as,

It gives value of

Therefore,

Therefore,

Probability of hitting Bullseye atleast 5 times = 1

####2####

Find mean, variance and standard deviation?

----->From above information

#######

Note:-

Excel command for probability of binomial distribution

1) for

------>   

2) for

-------->