Question

Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean μ = 29.8 kilograms and standard deviation σ = 3.8 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

Answer 1

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We use these params to answer the question:

Mean = 29.8

Stdev = 3.8

)(a) x < 30

z < (30-29.8)/3.8 = 0.053

(b) 19 < x

(19-29.8)/3.8 < z

-2.842 < z

(c) 32 < x < 35

(32-29.8)/3.8 < z< (35-29.8)/3.8

0.579<z<1.368

d) -2.17<z

-2.17 = (x-29.8)/3.8

x = -2.17*3.8+29.8 = 21.554

21.554 < x

e. ) z < 1.28

x = 1.28*3.8 + 29.8 = 34.664

so, x<34.664

f ) -1.99<z<1.44

(-1.99*3.8+29.8) <z< (1.44*3.8 + 29.8)

= 22.238 <x<35.272