Use technology to find the indicated area under the standard Normal curve. Include an appropriately labeled sketch of the Normal curve and shade the appropriate region. a. Find the area in a standard Normal curve to the left of 1.63. b. Find the area in a standard Normal curve to the right of 1.63. Remember that the total area under the curve is 1. a. Which graph below shows the area in a standard Normal curve to the left of 1.63? A. 1.63 A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 25% of the way from the graph’s right edge, a vertical line segment with labeled horizontal coordinate 1.63 extends from the horizontal axis to the curve. The area below the curve and to the left of the vertical line segment is shaded. Your answer is correct. B. 1.63 A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 25% of the way from the graph’s right edge, a vertical line segment with labeled horizontal coordinate 1.63 extends from the horizontal axis to the curve. The area below the curve and to the right of the vertical line segment is shaded. C. -1.631.63 A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately 25% of the way from the left and right edges of the graph, two vertical line segments with respective labeled horizontal coordinates negative 1.63 and 1.63 extend from the horizontal axis to the curve. The area below the curve between the segment at negative 1.63 and the segment at 1.63 is shaded. D. -1.631.63 A graph contains a Normal curve, plotted over a horizontal axis, which extends between the left and right edges of the graph and has a peak at the horizontal center. Approximately ALTp% of the way from the graph’s left and right edges of the graph, two vertical line segments with respective labeled horizontal coordinates negative 1.63 and 1.63 extend from the horizontal axis to the curve. The area below the curve to the left of the segment at negative 1.63 and the area below the curve to the right of the segment at 1.63 are shaded. The area in a standard Normal curve to the left of 1.63 is 0.950.95. (Round to four decimal places as needed.)
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!
a.
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Find the area in a standard Normal curve to the left of
1.63.
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b.
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Find the area in a standard Normal curve to the right of
1.63.
Remember that the total area under the curve is 1. |
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