Question 1152881: Assume that 17% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below, rounded to four decimal places:
a. There are some lefties (≥1) among the 5 people.
b. There are exactly 3 lefties in the group.
c. There are at least 4 lefties in the group.
d. There are no more than 2 lefties in the group.
e. How many lefties do you expect?
f. With what standard deviation?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
It is a binomial distribution type problem.
I will use a Technology to solve it quickly.
I will use the Excel standard function BINOM.DIST to facilitate calculations.
It has the analogue --- the standard function binompdf in pocket calculators TI-83 and TI-84.
(a) P =  = 1 -  = 1 - BINOM.DIST(0,5,0.2,FALSE) = 0.67232.
(b) P =  = BINOM.DIST(3,5,0.2,FALSE) = 0.0512.
(c) P =  = 1 -  = 1 - BINOM.DIST(3,5,0.2,TRUE) = 0.00672.
(d) P =  = BINOM.DIST(2,5,0.2,TRUE) = 0.94208.
On Excel function BINOM.DIST, see its description everywhere, for example
https://support.office.com/en-us/article/binom-dist-function-c5ae37b6-f39c-4be2-94c2-509a1480770c
On binompdf function for pocket calculators TI-83 and TI-84 see the link
http://users.rowan.edu/~schultzl/ti/binomial.pdf
-----------------
If you want to learn in more details on how to use this Technology, look into the lessons
- How to calculate Binomial probabilities using Technology
- Solving problems on Binomial distribution with Technology
in this site.
Look also into this links to the recently solved problem
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1152847.html
https://www.algebra.com/algebra/homework/Probability-and-statistics/Probability-and-statistics.faq.question.1152847.html
|
|
|
