Use the Empirical Rule to answer the questions below: The distribution of weight

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 7.4 pounds and a standard deviation of 0.7 pounds 1. What percent of newborn babies weigh more than 8.1 pounds? 15.8713% 2. The middle 95% of newborn babies weigh between 6128 # and 8.872 # pounds. 3. What percent of newborn babies weigh less than 6 pounds? 2.28 -% 4. Approximately 50% of newborn babies weigh more than 7.4 pounds. 5. What percent of newborn babies weigh between 6.7 and 9.5 pounds? 84-ja%

Explanation / Answer

Ans:

The empirical rule shows that 68% will fall within the first standard deviation, 95% within the first two standard deviations, and 99.7% will fall within the first three standard deviations of the distribution's average.

1)8.1 is one standard deviation ab0ve the mean.

As, 68% lies within one standard deviation,so 32% lies outside,(1-0.68)/2=0.16 or 16% lies above one standard deviation of the mean.

16%

2)95% lies within 2 standard deviations of the mean.

lower limit=7.4-2*0.7=6

upper limit=7.4+2*0.7=8.8

3)95% falls within 2 standard deviations,so 0.05 falls outside,hence,(1-0.95)/2=0.025 or 2.5% falls below 6

2.5%

4)7.4

5)6.7 is one standard deviation below the mean and 9.5 is 3 standard deviations above the mean.

area between 6.7 and 7.4 will be approximately=0.68/2=0.34

area between 7.4 and 9.5 will be approximately=0.997/2=0.4985

So,total area between 6.7 and 9.5 will be =0.34+0.4985=0.8385 or 83.85%

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.