Consider babies born in the \"normal\" range of 37—43 weeks gestational age. Ext
ID: 3326908 • Letter: C
Question
Consider babies born in the "normal" range of 37—43 weeks gestational age. Extensive data support the assumption that for such babies born in the United States, birth weight is normally distributed with mean 3432 g and standard deviation 482 g. (Round your answers to four decimal places.)
(a) What is the probability that the birth weight of a randomly selected baby of this type exceeds 4000 g?
P(weight > 4000 g) =
Is between 3000 and 4000 g?
P(3000 g weight 4000 g) =
(b) What is the probability that the birth weight of a randomly selected baby of this type is either less than 2000 g or greater than 5000 g?
P(weight < 2000 g or weight > 5000 g) =
(c) What is the probability that the birth weight of a randomly selected baby of this type exceeds 6 lb? (Hint: 1 lb = 453.6 g.)
P(weight > 6 lbs) =
Explanation / Answer
Result:
Consider babies born in the "normal" range of 37—43 weeks gestational age. Extensive data support the assumption that for such babies born in the United States, birth weight is normally distributed with mean 3432 g and standard deviation 482 g. (Round your answers to four decimal places.)
(a) What is the probability that the birth weight of a randomly selected baby of this type exceeds 4000 g?
P(weight > 4000 g) =
z value for 4000, z =(4000-3432)/482 = 1.18
P(weight > 4000 g) =P( z > 1.18)
=0.1190
Is between 3000 and 4000 g?
P(3000 g weight 4000 g) =
z value for 3000, z =(3000-3432)/482 = -0.90
P(3000 g weight 4000 g) = P( -0.90<z<1.18)
=P( z < 1.18)-P( z< -0.90)
= 0.881- 0.1841
=0.6969
(b) What is the probability that the birth weight of a randomly selected baby of this type is either less than 2000 g or greater than 5000 g?
P(weight < 2000 g or weight > 5000 g) =
z value for 2000, z =(2000-3432)/482 = -2.97
z value for 5000, z =(5000-3432)/482 = 3.25
P(weight < 2000 g or weight > 5000 g) =P( z < -2.97 or P( z >3.25)
= 0.0015+ 0.0006
=0.0021
(c) What is the probability that the birth weight of a randomly selected baby of this type exceeds 6 lb? (Hint: 1 lb = 453.6 g.)
P(weight > 6 lbs) =
6 lbs = 6*453.6 =2721.6g
z value for 2721.6, z =(2721.6-3432)/482 = -1.47
P(weight > 6 lbs) = P( z > -1.47)
= 0.9292