| Parameters | seconds |
|---|---|
| mean | μ = 172 |
| standard deviation | σ = 29 |
Given the parameters for aircraft strobe lights in the table to the right,
a. What is the probability that
the time between flashes for 1 randomly chosen strobe light
will exceed 4.00 seconds?
Use the z formula the same way we learned in Chapter 6-3
z = (4.00 - 3.00) ÷ (0.40) = 1.00 ÷ 0.40 = 2.50 (round z to 2 decimals places)
P(z < 2.50) = 0.9938 = 99.38% (Table A-2)
The probability that the time between flashes for 1 randomly chosen strobe light will exceed 4.00 seconds is 0.62% (100% - 99.38%)
b. What is the probability that the mean time between flashes for 60 randomly chosen strobe lights will exceed 4.00 seconds
Remember to use the modified z formula when n > 1
z = (4.00 - 3.00) ÷ (0.40 ÷ √60) = 1.00 ÷ (0.40 ÷ 0.0516 ) = 19.36
P(z < 19.36) = 0.9999 = 99.99%
The probability that the time between flashes for 60 randomly chosen strobe lights will exceed 4.00 seconds is 0.01% (100% - 99.99%)
c. Since stobe lights on aircraft are intended to help pilots recognize other aircraft, which is more relevant?
probability for individual strobe lights or the probability for a group of 60 strobe lights?
Since pilots look at individual strobe lights, the probability for individual strobe lights is more important than the probability for a group of strobe lights.