Question

Some sources report that the weights of full-term newborn babies have a mean of 7 pounds and a standard deviation of 0.6 pound and are Normally distributed. What is the probability that one randomly selected newborn baby will have a weight over 8 pounds? What is the probability the average of four babies' weights will be over 8 pounds? Explain the difference between parts 1 and 2.

Answer 1

Solution :

mean = = 7

standard deviation = = 0.6

1) P(x >8 ) = 1 - p( x< 8 )

=1- p [(x - ) / < (8 -7) /0.6 ]

=1- P(z < 1.67)

= 1 - 0.9525 = 0.0475

probability = 0.0475

2)

n = 4

=   = 7

= / n = 0.6 / 4 = 0.3

P( > 8) = 1 - P( < 8)

= 1 - P[( - ) / < (8 -7 ) /0.3 ]

= 1 - P(z < 3.33 )

= 1 - 0.9996 = 0.0004

Probability = 0.0004

Part (1) one newborn babies weight probability greater than ,part (2) four newborn babies weights will be over 8 pounds.