Question

The weights of newborn children in the United States vary according to the Normal distribution with mean 7.5 pounds and standard deviation 1.25 pounds. The government classifies a newborn as having low birth weight if the weight is less than 5.5 pounds. A study of learning in early childhood chooses an SRS of 3 children.

1. Is it okay to use normal calculations for this problem? Explain

2. Describe the sampling distribution.

3. What is the probability that the mean birth weight of an SRS of 3 children is less than 5.5 pounds? Draw and shade the appropriate normal curve and find the probability. You must find a z-score and write a conclusion in context.

Answer 1

1:

It is given that distribytion of weight of newborn children is normally distributed so even though sample size is only three according to central limit theorem sampling distribution of sample mean will be approximately normal.

Answer: Yes, it is okay to use normal calculations for this problem.

2:

3:

Conclusion: There is only 0.28% chance that the mean birth weight of an SRS of 3 children is less than 5.5 pounds.

Following is the curve:

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