Fawns between 1 and 5 months old have a body weight that is approximately normal
ID: 3329624 • Letter: F
Question
Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean = 29.0 kilograms and standard deviation = 4.8 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 3.13 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.Yes. This weight is 1.56 standard deviations below the mean; 14 kg is an unusually low weight for a fawn. No. This weight is 3.13 standard deviations below the mean; 14 kg is a normal weight for a fawn.No. This weight is 3.13 standard deviations above the mean; 14 kg is an unusually high weight for a fawn.No. This weight is 1.56 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 large positive z, such as 3.It would have a z of 0. It would have a negative z, such as 2.
Explanation / Answer
as we know that z=(X-mean)/std deviation
a)X<30
z<(30-29)/4.8 =z<0.2083
b)19<x
(19-30)/4.8<z
-2.29<z
c)32<x<35
0.42<z<1.04
d)-2.17<z
29-2.17*4.8<x
18.58<x
e)z<1.28
x<35.14
f)
-1.99<x<1.44
19.45<z<35.91
g)Yes. This weight is 3.13 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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