Question

14)The average weight of a newborn baby is 7.9 pounds with standard deviation 0.7 pounds. Suppose the weight of babies is approximately Normally distributed.

a) What percentage of babies will have a birth weight between 6.5 and 9.3 pounds? Round to 2 decimals.

b)If a newborn’s weight is in the top 5% of all babies, then what is their weight at birth? Round to 2 decimals

Answer 1

Solution :

Given that ,

mean = = 7.9

standard deviation = = 0.7

P(6.5< x <9.3 ) = P[(6.5 -7.9) / 0.7< (x - ) / < (9.3-7.9) /0.7 )]

= P( -2< Z < 2)

= P(Z 2< ) - P(Z <-2 )

Using z table   

= 0.9772-0.0228

= 0.9544

answer=95.44%

(b)

Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05

= P(Z < z ) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.64 ) = 0.95  

z = 1.64 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.64*0.7+7.9

x= 9.0480

x=9 .05