The weights for newbom babies is approximately normally distributed with a mean

Question

The weights for newbom babies is approximately normally distributed with a mean of 7 pounds and a standard deviation of 1.7 pounds. Consider a group of 1100 newborn babies: 1. How many would you expect to weigh between 3 and 7 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 7 and 8 pounds? Get help: Video Read 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 Points possible: 1 Untimited attempts. Submit MacBook Pro 0

Explanation / Answer

Solution :

Given that mean ? = 7 , standard deviation ? = 1.7 and n = 1100

1. P(3 < x < 7) = P((x - ?)/? < Z < (x - ?)/?)

= P((3 - 7)/1.7 < Z < (7 - 7)/1.7)

= P(-2.3529 < Z < 0)

= 0.4906
  
2. P(x < 5) = P((x - ?)/? < (5 - 7)/1.7)

= P(z < -1.1765)

= 0.1190

3. P(x > 4) = P((x - ?)/? > (4 - 7)/1.7)

= P(Z > -1.7647)

= 0.9608

4. P(7 < x < 8) = P((x - ?)/? < Z < (x - ?)/?)

= P((7 - 7)/1.7 < Z < (8 - 7)/1.7)

= P(0 < Z < 0.5882)

= 0.2224

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