A safety light is designed so that the times between flashes are normally distri

Question

A safety light is designed so that the times between flashes are normally distributed with a mean of 3.00 and a standard deviation of 0.70 s. a. Find the probability that an individual is greater than an individual is greater than 4.00 s. b. Find the probability that the mean for 50 randomly selected times is greater than 4.00 s. c. Given that the light is intended to help people see and obstruction, which result is more relevant for assessing the safety of the light? a. The probability is approximately b. The probability is approximately c. Choose the correct answer below. A. Part (b) is more significant because the times of a single strobe is important. B. Part (a) is more significant because the times of a single strobe is important. C. Part (a) is more significant because the average times for a sample is important. D. Part (b) is more significant because the average times for a sample is important.

Explanation / Answer

a. Find the probability that an individual time is greater than 4 seconds

z(4) = (4 - 3)/0.7 = 1.43

P(x >4) = P(z > 1.43) = 1 - P(z < 1.43) = 1 - 0.9236 = 0.0764
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b. Find the probability that the mean for 50 randomly selected times is greater than 4 seconds

z(4) = (4 - 3)/[0.7/sqrt(50)} = 10.1116

P(x > 4) = P(z > 10.1116) = 1 - P(z < 10.1116) = 1 - 0.9999999 = 0.0001

c) Option D because in part (a) we are measuring only one value while in (b) we are dealing with a large sample which can tell us average time for the population.

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