Question

Daily commute time is normally distributed with mean=40 minutes and standard deviation=8 minutes. For 16 days of travel, what is the probability of an average commute time greater than 35? B. A cup holds 18 ozs. The beer vending machine has an adjustable mean and a standard deviation equal to .2 oz. What should the mean be set to so that the cup overflows only 2.5% of the time? C. The probability that Rutgers soccer team wins a game is .6. What is the probability they win 10 or more of the 14 games?

Answer 1

a) µ = 40

sd = 8

                        

                         = P(Z > -0.63)

                         = 1 - P(Z < -0.63)

                         = 1 - 0.2643

                         = 0.7357

b) sd = 0.2

or, µ = 18 - 0.2 * 1.96

or, µ = 17.608

c) p = 0.6

n = 14

This is a binomial distribution

P(X = x) = 14Cx * 0.6^x * (1 - 0.6)^14-x

P(X > 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14)

                = 14C10 * 0.6¹⁰ * 0.4⁴ + 14C11 * 0.6¹¹ * 0.4³ + 14C12 * 0.6¹² * 0.4² + 14C13 * 0.6¹³ * 0.4^! + 14C14 * 0.6¹⁴ * 0.4⁰

              = 0.1549