SOLUTION: The weights for newborn babies is approximately normally distributed with a mean of 6.5 pounds and a standard deviation of 1.8 pounds Consider a group of 1300 newborn babies

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Question 1205250: The weights for newborn babies is approximately normally distributed with a mean of 6.5 pounds and a standard deviation of 1.8 pounds
Consider a group of 1300 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 6 pounds?
3. How many would you expect to weigh more than 4 pounds?
4. How many would you expect to weigh between 6.5 and 10 pounds?

Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!



given:
mean, mu+=+6.5 pounds
standard deviation, sigma+=+1.8 pounds

a normal distribution formula:
z=%28x-mu%29%2Fsigma

1. How many would you expect to weigh between 3+and 7 pounds?
P%283%3C=x%3C=7%29
=P%28%283-6.5%29%2F1.8%3C=z%3C=%287-6.5%29%2F1.8%29
=P%28-1.9444444444444446%3C=z%3C=0.2777777777777778%29
=P%28z%3C=0.2777777777777778%29+-P%28z%3C-1.9444444444444446%29
=0.609409-0.0259209
=0.5834881
=58.35% => answer
Consider a group of 1300 newborn babies, then 1300%2A0.5834881=758.53453≈758 babies expected to weigh between 3+and 7 pounds

2. How many would you expect to weigh less than 6 pounds?

P%28x%3C6%29=P%28z%3E%286-6.5%29%2F1.8%29=P%28z%3C+-0.2777777777777778%29=0.390591=39.06%=> answer
1300%2A0.390591≈507 babies expected to weigh less than 6 pounds

3. How many would you expect to weigh more than 4 pounds?
P%28x%3E4%29=P%28z%3C%284-6.5%29%2F1.8%29=P%28z%3E-1.+38889%29=0.917567=91.76% => answer
1300%2A0.917567≈1192 babies expected to weigh more than 4 pounds

4. How many would you expect to weigh between 6.5 and 10 pounds?

P%286.5%3C=x%3C=10%29
=P%28%286.5-6.5%29%2F1.8%3C=z%3C=%2810-6.5%29%2F1.8%29
=P%280%3C=z%3C=1.9444444444444446%29
=P%28z%3C=1.9444444444444446%29-P%28z%3E0%29
=0.974079-0.5
=0.4741
=47.41% => answer
1300%2A0.4741≈616 babies expected to weigh between 6.5 and 10 pounds