Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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.