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.	271 141 309 245

(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
1	2	3	4

(b) Do the probabilities add up to 1? Why should they?

1) No, because they do not cover the entire sample space.

2) Yes, because they cover the entire sample space.   

3) Yes, because they do not cover the entire sample space.

4) No, because they cover the entire sample space.

What is the sample space in this problem?

A) 12AM-12PM

B) 6AM-6PM

C) 6AM-12Am

D) the entire day

Answer 1

(a)

Probability that an investor has a best idea during each time interval is given as follows:

6 AM - 12 PM	12 PM - 6 PM	6 PM - 12 AM	12 AM - 6 AM
271/966 = 0.281	141/966 = 0.146	309/966 = 0.320	245/966 = 0.254

(b)

Correct option:

(2) Yes, because they cover the entire sample space.

(c)

Correct option:

(D) the entire day