Question

Baby weights: the weight of male babies less than 2 months old in the United States is normally distributed with mean 11.5 pounds and standard deviation 2.5 pounds What proportion of babies weigh more than 13 pounds? What proportion of babies weigh less than 15 pounds? What proportion of babies weigh between 9 and 14 pounds? Is it unusual for a baby to weigh more than 15 pounds? Round 4 places

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	11.5
std deviation   =σ=	2.5000

1)

proportion of babies weigh more than 13 pounds:

probability =

P(X>13)

=

P(Z>0.6)=

1-P(Z<0.6)=

1-0.7257=

0.2743

2)

proportion of babies weigh less than 15 pounds:

probability =

P(X<15)

=

P(Z<1.4)=

0.9192

3)

proportion of babies weigh between 9 and 14 pounds :

probability =

P(9<X<14)

=

P(-1<Z<1)=

0.8413-0.1587=

0.6826

4)

as probability of having weight more than 15 pounds  is 0.0808 which is higher than 0.05 , therefore it is not unusual