Lab 9

Diana Pell

Procedure for Finding z Score from a Known Area (p = prob-ability)

=NORMSINV(p)

Procedure for Finding Values Using Excel

=NORMINV(p, µ, σ)

Procedure for Finding z Score from a Given Value (x = givenvalue, µ = mean, σ = standard deviation)

=STANDARDIZE(x, µ, σ)

Procedure for Finding Area from a Given z Score

=NORMSDIST(z)

Birth weights of babies in the United States can be modeled by a normaldistribution with mean 3300 grams (about 7.3 pounds) and standarddeviation 570 grams (about 1.3 pounds). Babies weighing less than 2500grams (about 5.5 pounds) are considered to be of low birth weight.

a) A graph of this normal distribution appears next. Shade in the regionwhose area corresponds to the probability that a randomly selectedbaby will have a low birth weight.

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Weights.jpg

b) Based on this shaded region (remembering that the total area underthe normal curve is 1), make an educated guess as to the proportionof babies born having a low birth weight.

c) Calculate the z-score for a birth weight of 2500 grams.

d) Determine the proportion of babies born having a low birth weight.

e) What proportion of babies does the normal distribution predict asweighing greater than 10 pounds (4536 grams) at birth?

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f) Determine the probability that a randomly selected baby weighs be-tween 3000 and 4000 grams at birth.

g) Data from the National Vital Statistics System indicate that in 2004there were 4,112,052 births in the United States. A total of 331,772babies were of low birth weight. From these data, what proportion ofbirths in 2004 were of low birth weight?

h) How does this proportion compare to the probability calculated by thenormal model in part d?

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i) Similarly, in 2004, 2,697,819 babies were born that weighed between3000 and 4000 grams. Calculate the proportion of these births between3000 and 4000 grams.

j) How does this proportion compare to the probability calculated by thenormal model in part f?

k) Based on your answers to parts h and j, does the normal model appearto be doing a reasonable job of predicting how often these outcomesoccur?

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l) What proportion of newborns weigh less than 5500 grams at birth?

m) How much would a baby have to weigh to be among the heaviest 10%of all newborns?

[Hint: What percentage weigh less than this?]

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