Question

A researcher measures the time (in seconds) it takes a sample of five participants to complete a memory task. It took four of the participants 7, 8, 8, and 9 seconds. If M = 9, then what must be the fifth time recorded?

Answer 1

1.41 seconds

Explanation:

The question did not specify what M = 9 signifies. To solve the question, it is assumed that M = 9 is the mean.

The mean of the time for the 5 participants is given as 9

Arithmetic mean(X)
`=(a_(1) + a_(2) + a_(3) + ... + a_(n))/(n)`

There are five participants who completed the memory task, hence, n = 5. The formula for mean now becomes;

Arithmetic mean(X)
`=(a_(1) + a_(2) + a_(3) + a_(4) + a_(5))/(n)`

9
`=(7 + 8 + 8 + 9 + a_(5) )/(5)`

32
`a_(5)` = 45

`a_(5)` =
`=(45)/(32)`

`a_(5)` = 1.41 seconds

The fifth time recorded is 1.41 seconds.