Question

Use the Empirical Rule to answer the questions below: The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.6 pounds and a standard deviation of 0.8 pounds.

1. What percent of newborn babies weigh more than 8.4 pounds? _____%

2. The middle 95% of newborn babies weigh between _____and____ pounds.

3. What percent of newborn babies weigh less than 6 pounds? ____%

4. Approximately 50% of newborn babies weigh more than____ pounds.

5. What percent of newborn babies weigh between 6.8 and 10 pounds? _____%

Answer 1

We are given that Weights are new boen babies are approximately Normal with $\mu=7.6,\sigma=0.8$ .

1. What percent of newborn babies weigh more than 8.4 pounds? 16%

2. The middle 95% of newborn babies weigh between 6.0and 9.2 pounds.

3. What percent of newborn babies weigh less than 6 pounds? 2.5%

4. Approximately 50% of newborn babies weigh more than 7.6 pounds.

5. What percent of newborn babies weigh between 6.8 and 10 pounds? 99%

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1. What percent of newborn babies weigh more than 8.4 pounds? 16%

Here 8.4 pounds is $\mu+1*\sigma$ and the required probability is $P(X>\mu+1*\sigma)$ . By Empirical rule we know that $P(\mu-\sigma <X<\mu+\sigma) \Rightarrow P(X>\mu+\sigma)=0.5-\frac{0.68}{2}=0.16$

2. The middle 95% of newborn babies weigh between 6.0and 9.2 pounds.

We know by Empirical rule that
* 2*C
covers 95% of the area and is symmetric. Therefore the limits are $7.6\pm 2*0.8=7.6\pm 1.6=(6,9.2)$

3. What percent of newborn babies weigh less than 6 pounds? 2.5%

6 pounds =$\mu-2*\sigma$. and from the previous quetion teh probability is 0.05/2=0.025

4. Approximately 50% of newborn babies weigh more than 7.6 pounds.

This is the mid point since P(X>$\mu$)=0.5 by definition.

5. What percent of newborn babies weigh between 6.8 and 10 pounds? 99%

6.8 and 10 pounds are $\mu\pm 3*\sigma$ and by empirical rule the area covered is 0.99