When he was 3 months old, Benjamin Chance weighed 13.4 pounds. The national aver

Question

When he was 3 months old, Benjamin Chance weighed 13.4 pounds. The national average for the weight of a 3-month-old baby is 12.5 pounds, with a standard deviation of 1.5 pounds.

a. Determine the z-score for Ben's weight, and write a sentence interpreting it.

z=___.

At three months, Benjamin Chance's weight was about _____ of a standard deviation (below/above) the average.

b. Determine what proportion of 3-month-olds weigh more than Ben. Be sure to state any assumptions you make in order to do this calculation. Round your answer to four decimal places. _____.

c. For a 6-month-old, the national average weight is 17.25 pounds, with a standard deviation of 2.0 pounds. Determine what Ben's weight would have to have been at the age of 6 months for him to be among the middle 68% of 6-month-old babies. Enter your answers in increasing order.

His weight would have to be between ____ pounds and ____ pounds.

Explanation / Answer

a.z =13.4-12.5/1.5=0.6

b. Now we need to find P(x>13.5) usingz score in a we get

P(z>0.6)= 0.2743

c. P(x1<x<x2)=0.68

nowwe know that from z table (-0.994<z<0.994)=0.68

so z1=x1-17.25/2=-0.994

so x1=15.262

and similarly x2=19.238

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