Question

The distribution of weights for 12 month old baby girls in the US is approximately normal with mean u = 21 pounds and standard deviation of 2.2 pounds.

a) if a 12 month old girl weighs 23.2 pounds, approximately what weight percentile is she in?

b) if a 12 month old girl is in the 16th percentile in weight, estimate her weight.

c) Estimate the weight of t 12 month old girl who is in the 25th percentile by weight.

d) Estimate the weight of a 12 month old girl who is in the 75th percentile by weight.

Answer 1

Solution:

Given that,

mean = = 21 pounds

standard deviation = = 2.2 pounds

a ) x = 23.2 pounds

Using z-score formula,

z = x -   /

= 23.2 - 21 / 2.2

= 2.2 / 2.2

= 1

z = 1

Using standard normal table,

= 0.8413

Percentile is = 84^th

b ) Percentile is = 16^th

P(Z < z) = 16%

P(Z < z) = 0.16

Using standard normal table,

P(Z < - 0.9945) = 0.16

z = - 0.99

Using z-score formula,

x = z * +

x = - 0.99 * 2.2 + 21

= 18.82

Weight = 18.82 pounds

c ) Percentile is = 25^th

P(Z < z) = 25%

P(Z < z) = 0.25

Using standard normal table,

P(Z < - 0.6745) = 0.16

z = - 0.67

Using z-score formula,

x = z * +

x = - 0.67 * 2.2 + 21

= 19.53

Weight = 19.53 pounds

d ) Percentile is = 75^th

P(Z < z) = 75%

P(Z < z) = 0.75

Using standard normal table,

P(Z < -0.6745) = 0.75

z = 0.67

Using z-score formula,

x = z * +

x = 0.67 * 2.2 + 21

= 22.47

Weight = 22.47 pounds