Question

I need help with a bionomial distribution.
It has 4 parts. Please help.
Six percent of people in a city have type O- blood. you randomly select 39 people in the city and ask them if their blood type is O-.
Can the normal distribution be used to approximate the binomial distribution?
A. Yes, because both np ≥ 5 and nq ≥ 5
B. No, because np < 5
C. No, because nq < 5
(a) find the probability that exactly 10 people say they have O- blood
What is the indicated probability?
(b)find the probability that at least 10 people say they have O- blood.

Answer 1

(c) find the probability that fewer than 10 people say they have O- blood.
(d) a blood drive would to get at least five donors with O- blood. There are 100 donors. What is the probability that there will not be enough O- blood donors?
Can the normal distribution be used to approximate the binomial distribution?
A. No, because np < 5
B. No, because nq < 5
C. Yes, because both np ≥ 5 and nq ≥ 5
What is the probability that there will not be enough O- blood donors?

Answer 2

so for the part where 39 people are randomly selected, what is n and what is p?

once you know those, you can calculate n*p and since p+q = 1, q = 1-p and you can calculate to see if n*q >= 5

Answer 3

n= 39 p=0.06 q=.94
np= 2.34
nq= 36.66

Answer 4

so you know how to answer that part, yes?

Answer 5

which part is giving you trouble?

Answer 6

yes, the part giving me trouble is finding the probability

Answer 7

is B. No, because np < 5?

Answer 8

good.

to find the probability, you'll need a calculator. do you have one? if so, what kind?

Answer 9

\[P(X=k)=\left(\begin{matrix}n \\ k\end{matrix}\right)\cdot p^k \cdot \left( 1-p \right)^{n-k}\]

Answer 10

i have a TI-84

Answer 11

2nd VARS will get you to distributions, correct?

Answer 12

Yes

Answer 13

from there, if you arrow down you'll find

binompdf(

and

binomcdf(


If you want to calculate the probability of a single value (like in part (a), P(X=10) ), use the

binompdf(

the inputs are n , p, x separated by commas.

in order to calculate, hit 2nd, VARS, arrrow down to binompdf( then hit enter
the hit 3, then 9 then , then . then 0 then 6 then , then 1 then 0 then enter.

Answer 14

no comma after the 3, sorry

should look like this:

binompdf(39,.06,10)

Answer 15

okay, i got 6.39 x 10^-5
which i converted to 0.0000639 because i need to round to seven decimal places

Answer 16

that's what i got too!

Answer 17

i also have to pick from a graph
would the normal distribution not be used to approximate the binomial distribution?

Answer 18

well, what did you get for the first part? remember that np < 5 so the normal isn't really appropriate.

you should have a histogram with x approximately equal to np as the tallest.

Answer 19

do you have pics of the graphs?

Answer 20

sorry, i have to go. good luck!