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<30 So (X- )/ <(30-28.5)/3 Hence Z<1.5/3 Z<0.5 (b) X>19 So (X- )/ > (19-28.5)/3 Z> -3.1... View the full answer