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	Number of Inventors
6 A.M.-12 noon 12 noon-6 P.M. 6 P.M.-12 midnight 12 midnight-6 A.M.	294 141 319 212

(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-12PM6AM-6PM    6AM-12AMthe entire day

Answer 1

GIVEN THAT

N= 966

Time of Day When Best Ideas Occur
Time	Number of Inventors
6 A.M.-12 noon 12 noon-6 P.M. 6 P.M.-12 midnight 12 midnight-6 A.M.	294 141 319 212

A) P (6 AM - 12 NOON = 294 / 966 =0.304

P( 12 NOON - 6 PM ) = 141 / 966 = 0.146

P( 6 PM - 12 MID NIGHT) = 319 / 966 = 0.330

P ( 12 MID NIGHT - 6 AM) = 212 / 966 = 0.2195 = 0.220

6AM-12PM	12PM-6PM	6PM-12AM	12AM-6AM
0.304	0.146	0.330	0.220

B) 0.304 + 0.146 + 0.330 + 0.220 = 1

YES, BECAUSE THEY COVER THE ENTIRE SAMPLE SPACE

OPTION B IS CORRECT

C) SAMPLE SPACE = 6 AM - 6AM = THE ENTIRE DAY

OPTION D IS CORRECT