In a pediatrician’s office, the probability of a “no show” for any appointment

In a pediatrician’s office, the probability of a “no show” for any appointment

Subject: Mathematics / Statistics
Question
In a pediatrician’s office, the probability of a “no show” for any appointment in a given day is 0.10. Suppose here are 10 appointments for one day.

a. what is the random variable in this situation?

“no show” for nay check-up appointment

b. What is defined as a “success” ?

A “no show” (I am having difficulty understand if a “no show” is a success OR if would be showing up for the appointment, please explain).

c. What is the probability of success?

P (s) = 0.10 ( OR P(s) =0.90 if the success is showing up)

d. What is defined as a failure?

Showing up for the appointment (OR a “no show”)

e. Calculate the probability of failure.

P(f) = 0.90 (OR for a “no show” P(f) = 0.10).

f. Write the probability mass (distribution) function.

P(x) = (10!/x!(10-X)!) * 0.10x*0.90(10-X)

FOR the remaining questions I am not sure how to complete them. I am having difficulty comprehending the no show part and what it means in regards to: what is a success, failure, and how to set up the equation. Can I use the binompdf or binomcdf on my graphing calculator, if yes, how do I know which numbers to use?

g. What is the probability that fewer than 5 don’t show?

h. What is the probability that at least 3 don’t show?

i. What is the probability that 7 don’t show?

j. What is the probability that between 3 and 9 don’t show?

k. What is the probability that the doctor sees every patient scheduled?

l. What is the expected number of no shows for a given day?

1 “no show”

m. What is the variance for the number or no shows?

n. What is the standard deviation for the number of no shows?