Use Empericial Rule

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 7.3 pounds and a standard deviation of 0.8 pounds.

1. What percent of newborn babies weigh more than 8.1 pounds? Correct%

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

3. What percent of newborn babies weigh less than 5.7 pounds? %

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

5. What percent of newborn babies weigh between 6.5 and 9.7 pounds? Correct%

Answer 1

mean = 7.3 = xbar

standard deviation = .8 = s

z = (8.1-7.3)/.8 = .8/.8 = 1

68% are within 1 standard deviation from the mean

68/2 = 34% are greater than 8.1 lbs.

95% are within 2 s = 2(.8) = 1.6 of 7.3

in the interval x= 7.3+/-1.6 = (5.7, 8.9)

z=(5.7-7.3)/.8 = 1.6/.8 = 2

95/2 = 47.5% weigh less than 5.7 lbs

50% weigh more than the mean x>7.3 (7.3, infinity)

P(6.5, 9.7) = ?

z= (6.5-7.3)/.8 = .-.8/,8 =-1

z = (9.7-7.3/.8 = 2.4/.8 = 3

from z=-1 to z=0 is 34%

from z=0 to z=3 is 99.7/2 = 49.85%

34+49.85 = 83.85%