Question

1. The weights of newborn children in the U.S. vary according to the normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government classifies a newborn as having low birth weight if the weight is less than 5.5 pounds.       

a) You choose 3 babies at random. What is the probability that their average birth weight is less than 5.5 pounds?

b) What is the third quartile of the distribution?

Answer 1

Solution :

Given that,

mean = = 7.5

standard deviation = = 1.25

n = 3

= 7.5

=  / n = 1.25/ 3=0.72

a.

P( <5.5 ) = P[( - ) / < (5.5-7.5) /0.72 ]

= P(z < -2.78)

Using z table  

= 0.0027   

probability= 0.0027

b.

Using standard normal table,

P(Z < z) = 75%( third quartile)

= P(Z < z) = 0.75  

= P(Z < 0.67) = 0.75

z = 0.67 Using standard normal table,

Using z-score formula  

= z * +   

=0.67*0.72+7.5

= 7.98