Question

Use the binomial formula for the following:

Incubators are expensive, so hospitals are faced with the issue of supply vs. demand. A hospital doesn’t want to purchase unnecessary incubators, but they definitely do not want to have a shortage. Covenant Medical Center in Levelland recently concluded that 4% of newborns require time in an incubator. If 10 babies are born within a certain time range, find the following:

a. What is the probability that exactly 1 will need an incubator?

b. What is the probability that at most 1 will need an incubator?

c. What is the probability that at least 1 will need an incubator?

d. If Covenant in Levelland only has 2 incubators, what is the probability that will experience a shortage of incubators?

Answer 1

Let, X is a random variable which denotes the number of newborns needed an incubator.

and p(probability of newborns require an incubator)=4%=0.04 { given in question}

so, q(probability of newborns wont require an incubator)=1-0.04=0.96

N=10

applying binomial theorem

a) exactly 1

=

=0.277

b) at most 1

=

=.6648+.277=.9418

c) at least 1

=1-0.6648

=.3352

d) Covenant in Levelland only has 2 incubators, the probability that will experience a shortage of incubators means when we require more than 2.

=1-0.6648-.277-0.05194 {here,

=0.00626 =0.05194 }