Question

6. Suppose that you choose a student at random, and let the random variable “H” represent the student’s studying time (in hours) last week. Suppose that “H” has a uniform distribution on the interval (25, 35). If you randomly select 10 students and that each person’s studying time follows this same probability distribution, independently from person to person, determine the probability that at least two of the students studied for more than 32 hours last week.  

Answer 1

X ~ U (25 , 35)

P(one student studies more than 32 hours) = P(X > 32)

                                                                     = (35 - 32) / (35 - 25)

                                                                     = 0.3

p = 0.3

n = 10

This is a binomial distribution

P(X = x) = 10Cx * 0.3^x * (1 - 0.3)^10-x

P(X > 2) = 1 - (P(X = 0) + P(X = 1))

              = 1 - (10C0 * 0.3⁰ * 0.7¹⁰ + 10C1 * 0.3¹ * 0.7⁹)

              = 1 - 0.1493

              = 0.8507