Question

The weights for newborn babies is approximately normally distributed with a mean of 6.4 pounds and a standard deviation of 1.4 pounds.

Consider a group of 1100 newborn babies:

1. How many would you expect to weigh between 4 and 8 pounds? 

2. How many would you expect to weigh less than 7 pounds? 

3. How many would you expect to weigh more than 6 pounds? 

4. How many would you expect to weigh between 6.4 and 10 pounds? 

Answer 1

Solution :

Given that ,

mean = = 6.4

standard deviation = = 1.4

1.

P(4 < x < 8) = P[(4 - 6.4)/ 1.4) < (x - ) /  < (8 - 6.4) / 1.4) ]

= P(-1.7143 < z < 1.1429)

= P(z < 1.1429) - P(z < -1.7143)

= 0.8735 - 0.0432

= 0.8303

would = 0.8303

2.

P(x < 7) = P[(x - ) / < (7 - 6.4) / 1.4]

= P(z < 0.4286)

= 0.6659

would = 0.6659

3.

P(x > 6) = 1 - P(x < 6)

= 1 - P[(x - ) / < (6 - 6.4) / 1.4]

= 1 - P(z < -0.2857)

= 1 - 0.3876

= 0.6124

would = 0.6124

4.

P(6.4 < x < 10) = P[(6.4 - 6.4)/ 1.4) < (x - ) /  < (10 - 6.4) / 1.4) ]

= P(0 < z < 2.5714)

= P(z < 2.5714) - P(z < 0.5)

= 0.9949 - 0.5

= 0.4949

would = 0.4949