Question

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

a. If a 12 month old baby girl weights 23.2 pounds, approximately what weight percentile is she in?

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

c. Estimate the weight of a 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?

Answer 1

Solution:

Given that,

mean = = 21

standard deviation = = 2.2 pounds.

Using standard normal table,

a ) Using z-score formula,

z = ( x -  / )

= ( 23.2 - 21 / 2.2 )

= 2.2 /2.2

= 1

Using standard normal table,

The weight percentile 84.13%

b )P(Z < z) = 16%

P(Z < z) = 0.16

P(Z < - 0.9945) = 0.16

z = - 0.99

Using z-score formula,

x = z * +

x =- 0.99 * 2.2 + 21

=18.82

weight is 18.82 pounds

c )P(Z < z) = 25%

P(Z < z) = 0.25

P(Z < *- 0.6745) = 0.25

z = - 0.67

Using z-score formula,

x = z * +

x =- 0.67 * 2.2 + 21

=19.53

weight is 19.53 pounds

d )P(Z < z) = 75%

P(Z < z) = 0.75

P(Z < *0.6745) = 0.75

z = 0.67

Using z-score formula,

x = z * +

x =0.67 * 2.2 + 21

=22.47

weight is 22.47 pounds