Question

Birth weights in the United States have a distribution that is approximately normal with a mean of 3396 g and a standard deviation of 576 g. Apply Table A-2 or statistics technology you can use to answer the following questions:

(a) One definition of a premature baby is the the birth weight is below 2500 g. If a baby is randomly selected, find the probability of a birth weight below 2500 g.

(b) Another definition of a premature baby is that the birth weight is in the bottom 10%. Find the birth weight that is the cutoff between the bottom 10% and the top 90%.

(c) A definition of a "very low birth weight" is one that is less than 1500 g. If a baby is randomly selected, find the probability of a "very low birth weight".

(d) If 25 babies are randomly selected, find the probability that the mean of their mean weight is greater than 3400 g.

Answer 1

mean = 3396

sd = 576

(a) P(x < 2500)

P(z < -1.556) = 1- P(z < 1.556) = 1- 0.9406 = 0.0594

P(x < 2500) = 0.0594

(b) P(z < Z) = 0.10

z = -1.282

x = 2657.6

(c) P(x <1500)

P(z < -3.292) = 1- P(z < 3.292) = 1- 0.9995 = 0.00049

P(x < 1500) = 0.00049

(d) P( > 3400)

P(z > 0.035) =  1- P(z < 3.292) = 1- 0.516 = 0.484

P( > 3400) = 0.484