Question

According to a mattress commercial, 30% of car accidents are due to lack of sleep. Suppose that on any given day 10 car accidents occur.

a) Calculate the probability that five of the accidents were due to lack of sleep. interpret the results
b) Calculate the probability that at least two accidents were caused by lack of sleep. interpret the results

Answer 1

n = 10, p = 0.3

This is binomial distribution hence:

a) P(x = 5) =

Hence, 0.1029 is the probability that out of 10 accidents occurred on a given day five were due to lack of sleep.

b) P(at least 2) = 1 - P(x < 2) = 1 - P(0) - P(1)

Hence, 0.8507 is the probability that out of 10 accidents occurred on a given day at least 2 due to lack of sleep.

Answers are rounded to 4 decimal places.

I hope this will help. thank you.