Answer:
0.04746
Explanation:
To answer this one needs to find the area under the standard normal curve to the left of 5 minutes when the mean is 4 minutes and the std. dev. is 0.6 minutes. Either use a table of z-scores or a calculator with probability distribution functions.
In this case I will use my old Texas Instruments TI-83 calculator. I select the normalcdf( function and type in the following arguments: :
normalcdf(-100, 5, 4, 0.6). The result is 0.952. This is the area under the curve to the left of x = 5. But we are interested in finding the probability that a conversation lasts longer than 5 minutes. To find this, subtract 0.952 from 1.000: 0.048. This is the area under the curve to the RIGHT of x = 5.
This 0.048 is closest to the first answer choice: 0.04746.