Respuesta :
Answer:
A) 0.947; B) 0.0392; C) 0.7257; D) 6th
Step-by-step explanation:
For part A,
We find the z-score for both of these values and subtract them; this will give us the area under the curve between the scores, which is the same as the probability between them.
[tex]z=\frac{X-\mu}{\sigma}\\\\z=\frac{1000-1252}{129}\text{ and } z=\frac{1500-1252}{129}\\\\z=\frac{-252}{129}\text{ and } z=\frac{248}{129}\\\\z=-1.95\text{ and }z=1.92[/tex]
Using a z-table, we see that the area to the right of z = -1.95 is 0.0256. The area to the right of z = 1.92 is 0.9726. This means the area between them is
0.9726 - 0.0256 = 0.947.
For part B,
To find the probability that fewer than 1025 chips are in the bag, we find the z-score:
[tex]z=\frac{X-\mu}{\sigma}=\frac{1025-1252}{129}=\frac{-227}{129}\\\\=-1.76[/tex]
Looking this number up in the z-table, we find the area under the curve to the left of, or less than, this is 0.0392.
For part C,
Once we find the z-score for the value 1175, the z-table chart will give us the area under the curve less than this. To find the proportion greater than this, we subtract from 1:
[tex]z=\frac{X-\mu}{\sigma}=\frac{1175-1252}{129}=\frac{-77}{129}=-0.60[/tex]
In the z-table, we see that the area under the curve less than this is 0.2743. This means that the area greater than this is 1-0.2743 = 0.7257.
For part D,
We again find the area under the curve less than this. This tells us the proportion of values that will be less than this; this will tell us the percentile value for this.
[tex]z=\frac{1050-1252}{129}=\frac{-202}{129}=-1.57[/tex]
In the z-table, we see the area to the right of this is 0.0582. This means that 5.82% of values are less than this; this means the value is the 5.82 percentile, which rounds to the 6th percentile.
