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. 295
138
311
222
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

Answer 1

`P(6am-12\ noon) = 0.305`

`P(12\ noon - 6pm) = 0.143`

`P(6pm-12\ midnight) = 0.322`

`P(12\ midnight - 6am) =0.230`

Explanation:

Given

`\begin{array}{cc}{Time} & {Inventors} & {6am - 12\ noon} & {295} & {12\ noon -6pm} & {138} & {6pm - 12\ midnight} & {311} & {12\ midnight - 6am} & {222} & {Total} & {966} \ \end{array}`

Required

The probability of each time interval

To do this, we simply divide the number of inventors in the interval by the total inventors (966)

So, we have:

`P(6am-12\ noon) = (6am-12\ noon)/(Total)`

`P(6am-12\ noon) = (295)/(966)`

`P(6am-12\ noon) = 0.305`

`P(12\ noon - 6pm) = (12\ noon - 6pm)/(Total)`

`P(12\ noon - 6pm) = (138)/(966)`

`P(12\ noon - 6pm) = 0.143`

`P(6pm-12\ midnight) = (6pm-12\ midnight)/(Total)`

`P(6pm-12\ midnight) = (311)/(966)`

`P(6pm-12\ midnight) = 0.322`

`P(12\ midnight - 6am) =(12\ midnight - 6am)/(Total)`

`P(12\ midnight - 6am) =(222)/(966)`

`P(12\ midnight - 6am) =0.230`