Question

The speeds of a number of bicycles have a normal distribution model with a mean of 83 km/hr and a standard deviation of 9.4 km/hr. Find the probability that a bicycle picked at random is travelling at more than 95 km/hr?

(a) 0.1587

(b) 0.38

(c) 0.49

(d) 0/278

I have been asked this question in an interview for job.

Origin of the question is Probability Distribution topic in section Discrete Probability of Discrete Mathematics

Answer 1

Correct choice is (b) 0.38

Explanation: Let x be the random variable that represents the speed of bicycle. x has μ = 90 and σ = 9.5. We have to find the probability that x is higher than 95 or P(x > 95). For x = 95, z = \(\frac{95 – 83}{9.4}\) = 1.27, P(x > 95) = P(z > 1.27) = [total area] – [area to the left of z = 1] = 1 – 0.620 = 0.38. The probability that a car selected at a random has a speed greater than 100 km/hr is equal to 0.38.