When do creative people get their best ideas? USA Today did a survey of 966 inve

Question

When do creative people get their best ideas? USA Today did a survey of 966 inventors (who hold U.S. patents) and obtained the following information Time of Day When Best Ideas Occur Time 6 A.M.-12 noon 12 noon-6 P.M 6 P.M.-12 midnight 12 midnight-6 A.M Number of Inventors 307 125 307 227 (a) Assuming that the time interval includes the left limit and all the times up to but not including the right limit, estimate the probability that an inventor has a best idea during each time interval: from 6 A.M. to 12 noon, from 12 noon to 6 P.M., from 6 P.M. to 12 midnight, from 12 midnight to 6 A.M. (Enter your answers to 3 decimal places.) 6AM-12PM 12PM-6PM 6PM-12AM 12AM-6AM (b) Do the probabilities add up to 1? Why should they? No, because they do not cover the entire sample space Yes, because they cover the entire sample space Yes, because they do not cover the entire sample space No, because they cover the entire sample space What is the sample space in this problem? 12AM-12PM 6AM-6PM 6AM-12AM the entire day

Explanation / Answer

a)
The total number of investors=307+125+307+227=966
P(6AM-12PM)=307/966=0.318
P(12PM-6PM)=125/966=0.129
P(6PM-12AM)=307/966=0.318
P(12AM-6AM)=227/966=0.235

b)
The probabilities add upto 1 because they cover entire sample space.

Option 'B' is correct.

Sample space in this problem is the entire day.

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