Fawns between 1 and 5 months old have a body weight that is approximately normal
ID: 3181804 • Letter: F
Question
Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean = 29.9 kilograms and standard deviation = 4.4 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 < 1
(b) 19 < x
2 < z
(c) 32 < x < 35
3 < z < 4
Convert the following z intervals to x intervals. (Round your answers to one decimal place.)
(d) 2.17 < z
5 < x
(e) z < 1.28
x < 6
(f) 1.99 < z < 1.44
7 < x < 8
(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 3.61 standard deviations below the mean; 14 kg is an unusually low weight for a fawn. Yes. This weight is 1.81 standard deviations below the mean; 14 kg is an unusually low weight for a fawn. No. This weight is 3.61 standard deviations below the mean; 14 kg is a normal weight for a fawn. No. This weight is 3.61 standard deviations above the mean; 14 kg is an unusually high weight for a fawn. No. This weight is 1.81 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 negative z, such as 2. It would have a z of 0.
The Standard Normal Distribution 68% of area 95% of area 99.7% of areaExplanation / Answer
1)
mean = 29.9 , std. deviation = 4.4
(a) x < 30
z( 30 ) = ( 30 - 29.9) / 4.4 = 0.022
z < 1
x(z) = std.deviation * z + mean
x( 1) = 4.4 * 1 + 29.9 = 34.3
(b) 19 < x
z( 19 ) = ( 19 - 29.9) / 4.4 = -2.47
2 < z
x(z) = std.deviation * z + mean
x( 2) = 4.4 * 2 + 29.9 = 38.7
(c) 32 < x < 35
z( 32 < z <35 ) = (( 32 - 29.9) / 4.4 < z <( 35 - 29.9) / 4.4) = (0.47 < z <1.16)
3 < z < 4
x(z) = std.deviation * z + mean
x( 3) = 4.4 * 3 + 29.9 = 43.1
x( 4) = 4.4 * 4 + 29.9 = 47.5
(43.1 < x < 47.5)
2)
(d) 2.17 < z
x(z) = std.deviation * z + mean
x( -2.17) = 4.4 * -2.17 + 29.9 = 20.3
5 < x
z( 5 ) = ( 5 - 29.9) / 4.4 = -5.6
(e) z < 1.28
x(z) = std.deviation * z + mean
x( 1.28) = 4.4 * 1.28 + 29.9 = 35.5
x < 6
z( 6 ) = ( 6 - 29.9) / 4.4 = -5.4
(f) 1.99 < z < 1.44
x(z) = std.deviation * z + mean
x( -1.99) = 4.4 * -1.99 + 29.9 = 21.1
x( 1.44) = 4.4 * 1.44 + 29.9 = 36.2
(43.1 < x < 47.5)
7 < x < 8
z( 7 < z < 8 ) = (( 7 - 29.9) / 4.4 < z <( 8 - 29.9) / 4.4) = (-5.2 < z < -4.9)
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