Question

According to a recent survey, 90% of students say that they do not get enough sleep. Assume the survey meets the conditions of a binomial experiment. Round your answers to three decimal places

In a random survey of 28 students, find the probability that exactly 26 of them will say that they do not get enough sleep:

In a random survey of 28 students, find the probability that more than 26 of them will say that they do not get enough sleep:

Answer 1

Ans.

n = 28 , p = 90% = 0.90

This is Binomial Probability. The pmf is

Where, n = No. of trials

p = Prob. of success in single trial

x = No. of success

We find probability using R:-

For Probability mass function

>dbinom(x,n,prob=p)

For Commulative distribution function

>pbinom(x,n,prob=p)

(a) Exactly 26 do not get enough sleep

> dbinom(26,28,prob=0.90)
[1] 0.2442289

Probability that exact 26 of them do not get enough sleep = 0.2442

(b). More than 26 do not get enough sleep

> 1-pbinom(26,28,prob=0.90)
[1] 0.215154

Probability that more than 26 of them do not get enough sleep = 0.2152