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In: Statistics and Probability

Question 10 The probability that a student uses Smarthinking Online Tutoring on a regular basis is...

Question 10

The probability that a student uses Smarthinking Online Tutoring on a regular basis is 0.44 . In a group of 18 students, what is the probability that exactly 6 of them use Smarthinking Online Tutoring on a regular basis?

Write only a number as your answer. Round to 4 decimal places (for example 0.2416). Do not write as a percentage.

Question 11

The probability that a randomly selected commuter listens to audiobooks during their commute is 0.44 . Suppose that a sample of 10 commuters is selected, what is the probability that at most 3 of them listen to audiobooks?

Write only a number as your answer. Round to 2 decimal places (for example 0.24). Do not write as a percentage.

Question 12

At a car rental agency, 0.34 of the cars are returned on time. A sample of 11 car rentals is studied. What is the probability that more than 3 of them are returned on time?

Write only a number as your answer. Round to 2 decimal places (for example 0.24). Do not write as a percentage.

Solutions

Expert Solution

We use Binomial distribution to solve the given problems:

FORMULA USED:

The probability of x successes out of n trials is,

where is the probability of success.

QUESTION 10:

GIVEN:

Number of students

Probability that a student uses Smart thinking Online Tutoring on a regular basis

CALCULATION:

The probability that exactly 6 of them use Smart thinking Online Tutoring on a regular basis out of 18 students is,

Thus the probability that exactly 6 of them use Smart thinking Online Tutoring on a regular basis is .

QUESTION 11:

GIVEN:

Number of commuters

Probability that a randomly selected commuter listens to audio books during their commute

CALCULATION:

The probability that at most 3 of them listen to audio books is,

  

Thus the probability that at most 3 of them listen to audio books is .

QUESTION 12:

GIVEN:

Number of car rentals

Probability that a randomly selected cars are returned on time

CALCULATION:

The probability that more than 3 of them are returned on time is,

  

  

Thus the probability that more than 3 of them are returned on time is .

orchestra answered 1 year ago
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