Question

The birth weight of babies is approximately LOGNORMALLY distributed, with a mean of 3732 grams and a standard deviation of 472 grams.

(a) What is the probability that a baby’s weight exceeds 5000g?
(b) What is the probability that a baby’s weight is between 3000g and 4000g?
(c) What are the 10th, 50th, and 95th percentile weights for a baby?

Answer 1

Solution :

Given that,

mean = = 3732

standard deviation = = 472

a ) P (x > 5000 )

= 1 - P (x < 5000 )

= 1 - P ( x -  / ) < ( 5000 - 3732 / 472)

= 1 - P ( z < 1268 / 472 )

= 1 - P ( z < 2.69)

Using z table

= 1 - 0.9964

= 0.0036

Probability = 0.0036

b ) P (3000 < x < 4000 )

P ( 3000 - 3732 / 472) < ( x -  / ) < ( 4000 - 3732 / 472)

P ( - 732 / 472 < z < 268 / 472 )

P (-1.55< z < 0.57 )

P ( z < 0.57 ) - P ( z < -1.55 )

Using z table

= 0.7157 - 0.0606

= 0.6551

Probability = 0.6551

c ) P(Z < z) = 10%

P(Z < z) = 0.10

P(Z < -1.28) = 0.10

z = -1.28

Using z-score formula,

x = z * +

x = -1.28* 472 + 3732

x = 3127.84

P(Z < z) = 50%

P(Z < z) = 0.50

P(Z < 0 ) = 0.50

z = 0

Using z-score formula,

x = z * +

x = 0 * 472 + 3732

x = 3732

P(Z < z) = 95%

P(Z < z) = 0.95

P(Z < 1.64) = 0.95

z = 1.64

Using z-score formula,

x = z * +

x = 1.64 * 472 + 3732

x = 4506.08