Question

Baby weights: The weight of male babies less than 2 months old in the United States is normally distributed with mean 11.4 pounds and standard deviation 2.9 pounds. Use Table A.2 to answer the following Part 1 What proportion of babies weigh more than 13 pounds? The proportion of babies weighing more than 13 pounds is 10.2912 | Part 2 What proportion of babies weigh less than 15 pounds? The proportion of babies weighing less than 15 pounds is 0.8925 Part 3 out of 4 What proportion of babies weigh between 10 and 12 pounds? The proportion of babies weighing between 10 and 12 pounds is

Answer 1

Given,

$\mu$ = 11.4 , $\sigma$ = 2.9

We convert this to standard normal as

P(X < x) = P(Z < x - $\mu$ / $\sigma$ )

a)

P(X > 13) = P(Z > (13 - 11.4) / 2.9)

= P(Z > 0.55)

= 0.2912

b)

P(X < 15) = P(Z < (15 - 11.4) / 2.9)

= P(Z < 1.24)

= 0.8925

c)

P(10 < X < 12) = P(X < 12 ) - P(X < 10)

= P(Z < (12 - 11.4) / 2.9) - P( Z < (10 - 11.4) / 29)

= P(Z < 0.21) - P(Z < -0.48)

= 0.5832 - 0.3156

= 0.2676