Question

Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean μ = 29.2 kilograms and standard deviation σ = 3.4 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 4.47 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.

Yes. This weight is 2.24 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.    

No. This weight is 4.47 standard deviations below the mean; 14 kg is a normal weight for a fawn.

No. This weight is 4.47 standard deviations above the mean; 14 kg is an unusually high weight for a fawn.

No. This weight is 2.24 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 negative z, such as −2.

It would have a z of 0.    

It would have a large positive z, such as 3.

Answer 1