Answer to Question #179447 in Statistics and Probability for Mathews

Question #179447

If it is estimated that 30% of all students who fall under the Business Economics and management departmebt at Richfield have driver's license. What is the probability of this in a sample of 10 students?

1. Exactly 4 have a driver's license?

2. At least 2 have a valid driver's license?

3. More than 9 have a valid driver's license?


1
Expert's answer
2021-04-15T06:49:57-0400

The probability that a student has a driver's license is "p=0.3". We will use a binomial distribution for this problem. Assume that a random variable "X" denotes a number of people that have driver's license. We have to calculate the following probabilities:

  1. "P(X=4)=C_{10}^4p^4(1-p)^6=\\frac{10!}{4!6!}(0.3)^4(0.7)^6\\approx0.2001" (it is rounded to 4 decimal places)
  2. "P(X\\geq2)=1-P(X<2)=1-P(X=0)-P(X=1)="

"=1-p^{10}-C_{10}^1p^9(1-p)=1-(0.3)^{10}-10\\cdot0.3^9\\cdot0.7\\approx0.9999"

3. "P(X>9)=P(X=10)=(1-p)^{10}=(0.7)^{10}\\approx0.0282"


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