1) Last year times by runners in a footrace were normally distributed with mean

Question

1) Last year times by runners in a footrace were normally distributed with mean 36 minutes and standard deviation 2.5 minutes. Race organizers wish to predict the smallest time T such that 95% of the runners will have finished the race by time T. Based on last year’s results, that time T is about

(a) 49.4 min (b) 43.5 min (c) 37.0 min (d) 40.1 min (e) 38.6 min

2) A continuous random variable X has a uniform distribution on the interval [3,3]. Sketch the graph of its density function. (sketch the graph and explain)

Explanation / Answer

We are allowed to answer 1 question at a time.

1) Given: µ = 36 minutes, = 2.5 minutes

P(X < x) = 0.95

The Z score at p = 0.95 is 1.64

Since Z = (X - µ)/ , Therefore (X - 36)/2.5 = 1.64. Solving X = (1.64*2.5) + 36 = 40.1 minutes (Option c)

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