A market research company employs a large number of typists to enter data into a computer database. The time taken for new typists to learn the computer system is known to have a Normal distribution with a mean of 2.167 hours and a standard deviation 20 minutes. A candidate is automatically hired if he or she learns the computer system in less than 100 minutes. A cut off time is set at the slowest 40% of the learning distributions. Anyone slower than this cut-off time is not hired
A. 0.023
B. 0.067
C. 0.159
D. 0.309
This is what I did. I first converted 2.167 hours to minutes.
2.167 hours= 130.02 minutes
Then entered the data in my calculator
normalcdf (-e99, 100, 130.02, 20)
=.0666
or .067.
Thus the answer is B. Tell me if I'm right and if I'm wrong can you help me figure out what I did wrong and how to approach the right answer. Thank you :)
Your approach is correct, and you have obtained the answer correctly as well.
To solve this problem, you converted the mean time from hours to minutes, which is 2.167 hours = 130.02 minutes. Then, using the normalcdf function on your calculator, you calculated the probability of a candidate learning the computer system in less than 100 minutes, given a mean of 130.02 minutes and a standard deviation of 20 minutes.
The result, approximately 0.0666 or 0.067 when rounded, represents the probability of a candidate being hired for learning the system in less than 100 minutes. Since the cut-off time is set at the slowest 40% of the learning distributions, any candidate slower than this cut-off time is not hired. This means that approximately 6.7% (or 0.067) of candidates will be hired.
Therefore, your answer of B. 0.067 is correct. Well done!