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Question

Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with

mean μ = 28.5 kilograms and standard deviation σ = 3.0 kilograms. Let x be the weight of a fawn in kilograms.


For parts (a), (b), and (c), convert the x intervals to z intervals. (For each answer, enter a number. Round your answers to two decimal places.)

(a)    x < 30

z < 


(b)    19 < x (Fill in the blank. A blank is represented by _____.)


_____ < z




(c)    32 < x < 35 (Fill in the blanks. A blank is represented by _____. There are two answer blanks.)


_____ < z < _____


first blank     

second blank     


For parts (d), (e), and (f), convert the z intervals to x intervals. (For each answer, enter a number. Round your answers to one decimal place.)

(d)    −2.17 < z (Fill in the blank. A blank is represented by _____.)


_____ < x




(e)    z < 1.28

x < 


(f)    −1.99 < z < 1.44 (Fill in the blanks. A blank is represented by _____. There are two answer blanks.)


_____ < x < _____


first blank     

second blank     


(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 4.83 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.

Yes. This weight is 2.42 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.    

No. This weight is 4.83 standard deviations below the mean; 14 kg is a normal weight for a fawn.

No. This weight is 4.83 standard deviations above the mean; 14 kg is an unusually high weight for a fawn.

No. This weight is 2.42 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.

Top Answer

(a) X&lt;30 So (X- )/ &lt;(30-28.5)/3 Hence Z&lt;1.5/3 Z&lt;0.5 (b) X&gt;19 So (X- )/ &gt; (19-28.5)/3 Z&gt; -3.1... View the full answer

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