Question

he weights for newborn babies is approximately normally distributed with a mean of 5.1 pounds and a standard deviation of 1.4 pounds. Consider a group of 1500 newborn babies: 1. How many would you expect to weigh between 3 and 6 pounds? 2. How many would you expect to weigh less than 5 pounds? 3. How many would you expect to weigh more than 4 pounds? 4. How many would you expect to weigh between 5.1 and 8 pounds? Get help: ReadVideo Box 1: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity Box 2: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity Box 3: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity Box 4: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172 Enter DNE for Does Not Exist, oo for Infinity

Answer 1

n = total number of newborn babies = 1500

Let random variable X : The weights for newborn babies

X is normally distributed with mean = and standard deviation =

1)

   where z is standard normal variable

= P(-1.5 < z < 0.64) (Round to 2 decimal)

= P(z < 0.64) - P(z < -1.5)

= 0.7389 - 0.0668 (From statistical table of z values)

= 0.6721

Number of newborn babies weigh between 3 and 6 pounds

= 1500 * 0.6721

= 1008.16

= 1008 (Round to nearest integer)

We would expect 1008 babies weigh between 3 and 6 pounds

2)

   where z is standard normal variable

= P(z < -0.07) (Round to 2 decimal)

= 0.4721 (From statistical table of z values)

Number of newborn babies weigh less than 5 pounds

= 1500 * 0.4721

= 708.15

= 708 (Round to nearest integer)

We would expect 708 babies weigh less than 5 pounds

3)

   where z is standard normal variable

= P(z > -0.79) (Round to 2 decimal)

= 1 - P(z < -0.79)

= 1 - 0.2148    (From statistical table of z values)

= 0.7852

Number of newborn babies weigh more than 4 pounds

= 1500 * 0.7852

= 1177.854   

= 1178    (Round to nearest integer)

We would expect 1178 babies weigh more than 4 pounds

4)

   where z is standard normal variable

= P(0< z <2.07) (Round to 2 decimal)

= P(z < 2.07) - P(z < 0)

= 0.9808 - 0.5 (From statistical table of z values)

= 0.4808

Number of newborn babies weigh between 3 and 6 pounds

= 1500 * 0.4808

= 721.2

= 721 (Round to nearest integer)

We would expect 721 babies weigh between 5.1 and 8 pounds