SOLUTION
We are told to translate; (x, y) to (x -8, y). This means we have to add - 8 to each value of x in P(-5,1), Q(-4,6), and R(-2,3).
In P(-5,1), x = -5 and y = 1
In Q(-4,6), x = -4 and y = 6 and
In R(-2,3), x = -2 and y = 3
For the dilation centered at the origin k =2, simply multiply the value of k, which is 2 into the translations.
Answer:
The proportion of the population that have a protein requirement less than 0.60 g P • kg-1 • d-1 is 0.239, that is, 239 persons for every 1000, or simply 23.9% of them.
Step-by-step explanation:
From the question, we have the following information:
We have here that protein requirements in adults is normally distributed with defined parameters. The question is about <em>the proportion</em> <em>of the population</em> that has a requirement less than .
For answering this, we need to calculate a <em>z-score</em> to obtain the probability of the value <em>x </em>in this distribution using a <em>standard normal table</em> available on the Internet or on any statistics book.
<h3>z-score</h3>A z-score is expressed as
For the given parameters, we have:
With this value for <em>z</em> at hand, we need to consult a standard normal table to determine what the probability of this value is.
The value for z = -0.7142857 is telling us that the requirement for protein is below the population mean (negative sign indicates this). However, most standard normal tables give a probability that a statistic is less than z and for values greater than the mean (in other words, positive values). To overcome this, we need to take the complement of the probability given for z-score z = 0.7142857, that is, subtract from 1 this probability, which is possible because the normal distribution is <em>symmetrical</em>.
Tables have values for <em>z</em> with two decimal places, then, for z = 0.7142857, we need to rewrite it as z = 0.71. For this value, the <em>standard normal table</em> gives a value of P(z<0.71) = 0.76115.
Therefore, the cumulative probability for values less than x = 0.60 which corresponds to a z-score = -0.7142857 is approximately:
(rounding to three decimal places)
That is, the proportion of the population that have a protein requirement less than 0.60 g P • kg-1 • d-1 is
See the graph below. The shaded area is the region that represents the proportion asked in the question.
