Answer:
The value for <em>k</em> is about k = 11.093kg.
Step-by-step explanation:
To answer this question, that is, P(x<k) = 0.85, we can use the standardized value for a raw score, or the formula for obtaining z-scores:
[1]
Where
is the raw score.
is the population mean.
is the population standard deviation.
In this case, we are asking to find a value x = k, so that 85% of the blocks have weights less than k (kg).
We have also to use the values for the <em>cumulative standard normal distribution</em> with and
to find the value of z that corresponds to a probability of 0.85.
First step: find the z that corresponds to the probability of 0.85.
To use the formula [1], as we previously mentioned, we first need to find the value of <em>z</em> that corresponds to a probability of 0.85 using the <em>cumulative standard normal distribution table</em> (available in any Statistics books or on the Internet). Then, for a cumulative probability of 0.85, the corresponding value for z = 1.03 (approximately).
Second step: solve the formula [1] for x.
Solving this formula for x, we have:
Then (without units):
So
Thus, this value for x = 11.093 equals the value for k (x = k) so that
Then
or
We can see the graph below showing this value of k = 11.093kg for which 85% of the blocks have weights less that it (x = k = 11.093kg).
