Fawns between 1 and 5 months old have a body weight that is approximately normal
ID: 2946405 • Letter: F
Question
Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean ? = 25.7 kilograms and standard deviation ? = 3.1 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 3.77 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.Yes. This weight is 1.89 standard deviations below the mean; 14 kg is an unusually low weight for a fawn. No. This weight is 3.77 standard deviations below the mean; 14 kg is a normal weight for a fawn.No. This weight is 3.77 standard deviations above the mean; 14 kg is an unusually high weight for a fawn.No. This weight is 1.89 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 negative z, such as ?2. It would have a large positive z, such as 3.
The Standard Normal Distribution = 0, ? = 1) 3 2 68% of area 95% of area 99.7% of areaExplanation / Answer
a) x < 30
z<(30-25.7)/3.1
z<1.39
b) 19 < x
(19-25.7)/3.1<z
= -2.16<z
c) 32 < x < 35
((32-25.7)/3.1<z<(35-25.7)/3.1
= -2.03<z<3
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