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.	298 142 315 211

(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

John runs a computer software store. Yesterday he counted 127 people who walked by the store, 58 of whom came into the store. Of the 58, only 21 bought something in the store. (Round your answers to two decimal places.)

(a) Estimate the probability that a person who walks by the store will enter the store.


(b) Estimate the probability that a person who walks into the store will buy something.


(c) Estimate the probability that a person who walks by the store will come in and buy something.


(d) Estimate the probability that a person who comes into the store will buy nothing.

Answer 1

1)

dividing each value with total frequency of 966:

Time	number	relative frequency
6 A.M.-12 noon	298	0.308
12 noon-6 P.M.	142	0.147
6 P.M.-12 midnight	315	0.326
12 midnight-6 A.M.	211	0.218
total	966

from above:

6 A.M.-12 noon	12 noon-6 P.M.	6 P.M.-12 midnight	12 midnight-6 A.M.
0.308	0.147	0.326	0.218

b)

Yes, because they cover the entire sample space

c)

the entire day

2)

a) probability that a person who walks by the store will enter the store=58/127=0.46

b) probability that a person who walks into the store will buy something=21/58=0.36

c)probability that a person who walks by the store will come in and buy something=21/127=0.17

d)

probability that a person who comes into the store will buy nothing=1-0.36 =0.64