two jets leave an airport at the same time in opposite directions. the first jet is traveling at 323 mph and the other at 347 mp
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Answer:
Only 0.0668 of the candidates, or 6.68%, have a GPA above 3.9.
Step-by-step explanation:
The GPA, according to the question, is a <em>random variable normally distributed</em>. A normal distribution is determined by its parameters. These parameters are the population mean, , and the population standard deviation,
. The normal distribution for GPA has a
, and
.
To find probabilities related to <em>normally distributed data</em>, we can use t<em>he standard normal distribution</em>. To use it, we first need to find the corresponding <em>standardized score</em> or z-score for the value we want to obtain the probability. This value, in this case, is <em>x</em> = 3.9. The related z-score or standardized value is given by the formula:
[1]
A z-score tells us the distance from the mean in standard deviations units. A <em>negative value</em> indicates that the value is <em>below </em>the mean. A <em>positive value</em> is, conversely, <em>above</em> the mean.
And we already have all the necessary data to use [1].
Thus
This value for <em>z</em> tells us that the "equivalent" raw score, <em>x</em> = 3.9, is <em>above</em> the mean, and it is at <em>1.5 standard deviations units</em> from the population mean.
We can find the probabilities for standardized values in <em>the cumulative standard normal table</em>, available on the Internet or in Statistic books (we can also use statistical packages or even spreadsheets).
To use the <em>cumulative standard normal table</em>, we have the z-score as an entry. With this value, we find the <em>z column</em> on this table, and, since it is z = 1.5, we only need to select the first column (which has two decimal places, that is, .00). Then, the cumulative probability for P(z<1.50) = 0.9332.
However, we are asked for the percent of candidates that have a GPA <em>above</em> 3.9 (z-score = 1.50). This probability is the complement of P(z<1.50) or 1 - P(z<1.50). Mathematically
(standardized)
That is, only 0.0668 of the candidates, or 6.68%, have a GPA above 3.9.
We can see this probability in the graph below.
