Answer:
a) Z for northern region = 1 , Z for southern region = -1.2
b) Southern region
Step-by-step explanation:
a) Z = (x – mean)/standard deviation
Le x be weight for birds
For the northern region
Z = (13 – 10)/3
Z = 1
For the southern region
Z = (13 – 16)/2.5
Z = -1.2
b) to find in what region is more likely to find a bird with 13 ounces, we calculate the probability for each z value
For the northern region
P (x>13) = P(z > 1)
Then we use the z table to find the area under the curve.
P (x>13) = 0.1587
For the southern region
P (x>13) = P(z > 1.2)
Then we use the z table to find the area under the curve.
P (x>13) = 0.8849
Is it more likely that a bird with a weight greater than 13 ounces lives in the southern region
it is more likely that a bird of this type with a weight greater than 13 ounces lives in the southern region
The z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma} \\\\x=raw\ score,\mu=mean,\sigma=standard\ deviation\\\\Given\ that\ \mu=10,\sigma=3\ for\ northern\ region.Also,\mu=16,\sigma=2.5\ for\ \\southern\ region\\\\a) For\ x=13\ in \ northern\ region:\\\\z=\frac{13-10}{3}=1 \\\\\\For\ x=13\ in \ southern\ region:\\\\z=\frac{13-16}{2.5}=-1.2 \\\\[/tex]
b) For the northern region, P(x > 13) = P(z > 1) = 1 - P(z < 1) = 1 - 0.8413 = 15.87%
For the southern region, P(x > 13) = P(z > -1.2) = 1 - P(z < -1.2) = 1 - 0.1314 = 86.86%
Hence it is more likely that a bird of this type with a weight greater than 13 ounces lives in the southern region
Find out more at: brainly.com/question/25012216
