83.4k views
5 votes
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

1 Answer

3 votes

Answer:

The value for k is about k = 11.093kg.

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:


\\ z = (x - \mu)/(\sigma) [1]

Where


\\ x is the raw score.


\\ \mu is the population mean.


\\ \sigma 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
\\ \mu = 0 and
\\ \sigma = 1 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:


\\ z = 1.03


\\ \mu = 11kg


\\ \sigma = 0.09kg

Then (without units):


\\ z = (x - \mu)/(\sigma)


\\ 1.03 = (x - 11)/(0.09)


\\ 1.03*0.09 = x - 11


\\ (1.03*0.09) + 11 = x

So


\\ x = (1.03*0.09) + 11


\\ x = 0.0927 + 11


\\ x = 11.0927 \approx 11.093 = k

Thus, this value for x = 11.093 equals the value for k (x = k) so that


\\ P(x<k) = 0.85

Then


\\ P(x<k=11.093) = 0.8493 \approx 0.85 or


\\ P(x<11.093) = 0.8493 \approx 0.85

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).

Suppose that a wall is constructed from concrete blocks where a block is a normal-example-1
User Tagar
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories