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

Answer:

1.41 seconds

Step-by-step 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) $=\frac{a_{1} + a_{2} + a_{3} + ... + a_{n}}{n}$

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

        Arithmetic mean(X) $=\frac{a_{1} + a_{2} + a_{3} + a_{4} + a_{5}}{n}$

                             9 $=\frac{7 + 8 + 8 + 9 + a_{5} }{5}$

                              32$a_{5}$ = 45

                              $a_{5}$ = $=\frac{45}{32}$

                              $a_{5}$ = 1.41 seconds

The fifth time recorded is 1.41 seconds.