DESCRIPTIVE STATISTICS

Question

Using all 1991 birth records in the computerized national birth certificate registry compiled by the National Center for Health Statistics (NCHS), statisticians Traci Clemons and Marcello Pagano found that the birth weights of babies in the United States are not symmetric (“Are babies normal?” The American Statistician, Nov 1999, 53:4). However, they also found that when infants born outside of the “typical” 37–43 weeks and infants born to mothers with a history of diabetes are excluded, the birth weights of the remaining infants do follow a Normal model with mean μ = 3432 g and standard deviation σ = 482 g. The following questions refer to infants born from 37 to 43 weeks whose mothers did not have a history of diabetes.

Compute the z-score of an infant who weighs 4573 g. (Round your answer to two decimal places.)

Approximately what fraction of infants would you expect to have birth weights between 2750 g and 4560 g? (Express your answer as a decimal, not a percent, and round to three decimal places.)

Approximately what fraction of infants would you expect to have birth weights below 2750 g? (Express your answer as a decimal, not a percent, and round to three decimal places.)

A medical researcher wishes to study infants with low birth weights and seeks infants with birth weights among the lowest 7%. Below what weight must an infant's birth weight be in order for the infant be included in the study? (Round your answer to the nearest gram.)

g

Answer 1

Hope you have access to a z-score table for the Normal Distribution.

z score = (Value - Mean)/Std. Dev'n. = (x - µ)/σ.

1) z₄₅₇₃ = (4573 - 3432)/482 = 1141/482 = 2.367 (2.37 to two dec. places).

2) z₂₇₅₀ = (2750 - 3432)/482 = -682/482 = -1.415 (lies between -1.41 and -1.42 on the table. Need to average out the two respective probabilities. S/B = 0.07855.

Do same for z₄₅₆₀. Subtract the two values obtained from the table to find probability of a wt. between 2750 and 4560 gms.

3) The table gives probabilities (area under the normal curve) to the left of the x value. Use answer from z₂₇₅₀ in question 2). Round as required.

4) z for 0.07 is ≈ -1.475

x = μ + zσ → x = 3432 +(-1.475)(482) = 2721 gms (rnd'd to nearest whole gm).