Question

The distribution of weights for 12 month old baby boys in the US is approximately normal with mean 22.5 pounds and a standard deviation of 2.2 pounds. a. if a 12 month old boy weights 20.3 pounds, what weight percentile is he in approximately. b. if a 12 month old boy is in the 84th percentile in weight, estimate his weight. c. Estimate the weight of a 12 month old boy who is in the 25th percentile by weight. d. Estimate the weight of a 12 month old boy who is in the 75 percentile by weight.

Answer 1

Solution:

Given that,

mean = = 22.5 pounds

standard deviation = = 2.2 pounds.

Using standard normal table,

a ) Using z-score formula,

z = ( x -  / )

= ( 20.3- 22.5 / 2.2 )

= - 2.2 /2.2

= - 1

Using standard normal table,

The weight percentile 15.87%

b )P(Z < z) = 84%

P(Z < z) = 0.84

P(Z < 0.9945) = 0.84

z = 0.99

Using z-score formula,

x = z * +

x = 0.99 * 2.2 + 22.5

=24.68

weight is 24.68 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 + 22.5

= 21.02

weight is 21.02 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 + 22.5

=23.97

weight is 23.97 pounds