Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean μ = 25.5 kilograms and standard deviation σ = 3.1 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 < ______(blank) (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
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Fawns between 1 and 5 months old have a body weight that is approximately
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 < ______(blank)(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 < _____(blank)(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.
(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.
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