# Question #6cce1

Nov 30, 2016

Please refer to the explanation below.

#### Explanation:

Hey! I was asked that type question in my exam!

So,
$Z = \frac{X - \mu}{\sigma}$
X is a particular number you're using.
Z is a standard Normal variable

72.9 minutes is the highest point in the graph above.

Step 1, you need to first find the probability (P) of taking 60 minutes to assemble.

So, to calculate P(taking 60 minutes),
$Z = \frac{60 - 72.9}{8.55} = 1.509$,
If $Z = 1.509 , t h e n P = 0.4343$ [You calculate this using the Normal Distribution table]

Please refer to the Normal Distribution table on Page 2 of this pdf file: http://www.nzqa.govt.nz/nqfdocs/ncea-resource/exams/2012/91267-frm-2012.pdf

So, The probability of taking 60 minutes to assemble is 0.4343.

You want to find P(less than 60 minutes),
so 0.5 (bottom 50% of graph) - 0.4343 = 0.0657.

The probability that it will take less than an hour to assemble the next piece of machinery is 0.0657.