Question

Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean μ = 27.9 kilograms and standard deviation σ = 3.2 kilograms. Let x be the weight of a fawn in kilograms. The Standard Normal Distribution (mu = 0, sigma = 1). A normal curve is graphed above a horizontal axis labeled z. There are 7 equally spaced labels on the axis; from left to right they are: -3, -2, -1, 0, 1, 2 and 3. The curve enters the viewing window just above the axis at -3, reaches a peak at 0, and exits the viewing window just above the axis at 3. A dashed vertical line at 0 extends from the peak of the curve to the horizontal axis below. The area under the curve is divided into 5 regions. The first region is from z = -3 to -2 and is shaded yellow. The second region is from z = -2 to -1 and is shaded green. The third region is from z = -1 to 1 and is shaded blue. The fourth region is from z = 1 to 2 and is shaded green. The fifth region is from z = 2 to 3 and is shaded yellow. A line drawn between -1 and 1 is labeled 68% of area, a line drawn between -2 and 2 is labeled 95% of area, and a line drawn between -3 and 3 is labeled 99.7% of area.

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 4.34 standard deviations below the mean; 14 kg is an unusually low weight for a fawn. Yes. This weight is 2.17 standard deviations below the mean; 14 kg is an unusually low weight for a fawn. No. This weight is 4.34 standard deviations below the mean; 14 kg is a normal weight for a fawn. No. This weight is 4.34 standard deviations above the mean; 14 kg is an unusually high weight for a fawn. No. This weight is 2.17 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 z of 0. It would have a large positive z, such as 3. It would have a negative z, such as −2.

Answer 1

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