Fawns between 1 and 5 months old have a body weight that is approximately normal
ID: 3335650 • Letter: F
Question
Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean = 28.9 kilograms and standard deviation = 4.5 kilograms. Let x be the weight of a fawn in kilograms.
Convert the following x intervals to z intervals. (Round your answers to two decimal places.)
(a) x < 30
z <
(b) 19 < x
< z
(c) 32 < x < 35
< z <
Convert the following z intervals to x intervals. (Round your answers to one decimal place.)
(d) 2.17 < z
< x
(e) z < 1.28
x <
(f) 1.99 < z < 1.44
< x <
(g) If a fawn weighs 14 kilograms, would you say it is an unusually small animal? Explain using z values and the figure above.
Yes. This weight is 3.31 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.
Yes. This weight is 1.66 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.
No. This weight is 3.31 standard deviations below the mean; 14 kg is a normal weight for a fawn.
No. This weight is 3.31 standard deviations above the mean; 14 kg is an unusually high weight for a fawn.
No. This weight is 1.66 standard deviations above the mean; 14 kg is an unusually high weight for a fawn.
(h) If a fawn is unusually large, would you say that the z value for the weight of the fawn will be close to 0, 2, or 3? Explain.
It would have a z of 0.
It would have a large positive z, such as 3.
It would have a negative z, such as 2.
Explanation / Answer
Z = (X - mean)/standard deviation
A) X < 30
Z < (30 - 28.9)/4.5
= Z < 0.24
B) 19 < X
(19 - 28.9)/4.5 < X
-2.1 < X
C) 32 < X < 35
(32-28.9)/4.5 < Z < (35-28.9)/4.5
= 0.69 < Z < 1.36
D) -2.17 < Z
-2.17x4.5+28.9 < X
19.1 < X
E) z < 1.28
x < 1.28x4.5+28.9
X < 34.7
F) -1.99 < z < 1.44
-1.99x4.5+28.9 < X < 1.44x4.5+28.9
19.9 < X < 35.4
G) Yes. This weight is 3.31 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.
H) It would have a large positive z, such as 3
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