The reaction time of a driver to visual stimulus is normally distributed with a

Question

The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.4 seconds and a standard deviation of 0.05 seconds. (a) What is the probability that a reaction requires more than 0.5 seconds? (b) What is the probability that a reaction requires between 0.4 and 0.5 seconds? (c) What is the reaction time that is exceeded 90% of the time? Suppose that X is a binomial random variable with n = 100 and p = 0.1. (a) Compute the exact probability that X is less than 4. (b) Approximate the probability that X is less than 4 and compare to the result in part (a). The lifetime of a mechanical assembly in a vibration test is exponentially distributed with a mean of 400 hours. (a) What is the probability that an assembly on test fails in less than 100 hours? (b) What is the probability that an assembly operates for more than 500 hours before failure? (c) If an assembly has been on test for 400 hours without a failure, what is the probability of a failure in the next 100 hours? (d) If 10 assemblies are tested, what is the probability that at least one fails in less than 100 hours? Assume that the assemblies fail independently.

Explanation / Answer

4)

a. P(X<4) = P(X=0,1,2,3) = 0.0237
b.P(X<4) = P(Z< (4-100*.1)/sqrt(100*.1*.9) = P(Z<-2) = 1-.975 = .025

Notice small change in value, as part b is an approximation

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