It is generally believed that nearsightedness affects about 15% of children. A s
ID: 3040497 • Letter: I
Question
It is generally believed that nearsightedness affects about 15% of children. A school district gives vision tests to 111 incoming kindergarten children. Use the empirical rule (68%-95%-99.7% Rule) to determine what we might expect to see in samples of 111 children. Assume conditions are met! No need to draw the model, though if you find it easier to do so you may draw it by hand and attach a picture of your model using the picture button. Feel free to download the picture below to add your values to, then submit your updated screen shot. Empirical Model
Explanation / Answer
Ans:
Normal approximation:
mean=np=111*0.15=16.65
standard deviation=sqrt(111*0.15*0.85)=3.76
Number of childer having nearsightdness will follow normal distribution with mean 16.65 and std. dev=3.76
68% is the probability that number of affected children is within one standard deviation of the mean i.e.
16.65-3.76=12.89
16.65+3.76=20.41
95% is the probability that number of affected children is within two standard deviations of the mean i.e.
16.65-2*3.76=9.13
16.65+2*3.76=24.17
99.7% is the probability that number of affected children is within three standard deviations of the mean i.e.
16.65-3*3.76=5.37
16.65+3*3.76=27.93
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