Suppose that a wall is constructed from concrete blocks where a block is a normal random variable with mean 11 kg and standard deviation 0.09 kg. If 85% of the blocks have weights less than k kg, evaluate k

The value for k 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 cumulative standard normal distribution 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 z that corresponds to a probability of 0.85 using the cumulative standard normal distribution table (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).  

x-3y=4

step-by-step e