ab Area Under a Curve Technology FOR USE WITH LEssON 12-7 Statisticians use the

Question

ab Area Under a Curve Technology FOR USE WITH LEssON 12-7 Statisticians use the function Ax)- to model datasuch as height or birth weight. You can use the area under the graph of the function to find probabilities ACTIVITY In a given population, the weights of babies are normal mean, 3250 g. The standard deviation is 500 g. Find chosen at random weighs from 2250 g to 4250 g. ly distributed about the the probability that a baby Step 1 Find the z-scores of the lower Step 2 Enter x) as Y Adjust the window values and upper limits. z-score standard devintion NDOW Knin _-4.7 Xmax 4.7 21 Ymin -2 Yscl -.1 Step 3 Use the CALC feature and press 7 to access the Jfix )dx feature. Move the cursor until the lower limit is x =-2. Press upper limit is 2. Press ENTER Res. Move the cursor until the Lower Limit?99097 Upper Limitt The area under the curve from x =-2 to x = 2 is about 0-95. So the probability that a baby weighs from 2250 g to 4250 g is about 95%. EXERCISES Use the data and the function in the example. Find the probability that the weight of a baby chosen at random falls within each interval. 3. less than 1800 g 4. more than 4550 g 2. 4300-4500g 1. 3150-4150 g 5. For Exercises 1-4, estimate the number of babies within each interval from a population of 2400 babies that are normally distributed, with a mean of 45 months and a standard deviation of 5 months. Find the probability that a battery chosen at random will have each life span. a. 45-52 months 6. Manufacturing A battery company manufactures batteries having life spans b. 48-50 months Activity Lab Area Under a Curve 6

Explanation / Answer

Ans:

Given that

mean=3250

standard deviation=500

1)

z(3150)=(3150-3250)/500=-0.2

z(4150)=(4150-3250)/500=1.8

P(3150<=x<=4150)=P(-0.2<=z<=1.8)

=P(z<=-0.2)-P(z<=1.8)

=0.9641-0.4207

=0.5434

2)

z(4300)=(4300-3250)/500=2.1

z(4500)=(4500-3250)/500=2.5

P(4300<=x<=4500)=P(2.1<=z<=2.5)

=P(z<=2.5)-P(z<=2.1)

=0.9938-0.9821

   =0.0117

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