A researcher records the following time spent sleeping per night (in hours)in a group of participants: 5.8 1.8 (M SD).The researcher decides to categorize participants who sleep between 6 to 8 hours as moderate sleepers.What percentage of participants fell in this category?
A)about 39%
B)about 11%
C)about 35%
D)about 7%

Question

A researcher records the following time spent sleeping per night (in hours)in a group of participants: 5.8  1.8 (M  SD).The researcher decides to categorize participants who sleep between 6 to 8 hours as moderate sleepers.What percentage of participants fell in this category?
A)about 39% 
B)about 11% 
C)about 35% 
D)about 7%

Quizplus · Accepted Answer

To find the percentage of participants who sleep between 6 to 8 hours, we need to first calculate the mean of the data given by the researcher.

Mean = (5.8 + 11 + 1.8) / 3 = 6.533 hours

Now, we need to find out how many participants sleep between 6 to 8 hours.

Participants who sleep between 6 to 8 hours = (6.0 ≤ x ≤ 8.0) 
= (6.0 - 6.533) / 1.8 ≈ -0.296 
= (8.0 - 6.533) / 1.8 ≈ 0.815

Using a standard normal distribution table, we can find that the area between -0.296 and 0.815 is approximately 0.347. This means that about 34.7% of participants slept between 6 to 8 hours. Therefore, the best answer choice is C.

A Researcher Records the Following Time Spent Sleeping Per Night