Question

Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean μ = 25.9 kilograms and standard deviation σ = 3.5 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

Let X be the weight of a fawn in kilograms. X is normally distributed with mean μ = 25.9 kilograms and standard deviation σ = 3.5 kilograms.

(a) x < 30. The z score is

ans: z < 1.17

(b) 19 < x. The z score is

ans: -1.97 < z

(c) 32 < x < 35. The z score is

ans: 1.74 < z < 2.60

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 The value of X is

ans:  18.3 < x

(e) z < 1.28 The value of X is

ans: x < 30.4

(f) −1.99 < z < 1.44. The value of X is

ans:  18.9< x < 30.9