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 0.7 pounds.
1. What percent of newborn babies weigh more than 8.3 pounds? %
2. The middle 95% of newborn babies weigh between and pounds.
3. What percent of newborn babies weigh less than 6.2 pounds? %
4. Approximately 50% of newborn babies weigh more than pounds.
5. What percent of newborn babies weigh between 6.9 and 9.7 pounds? %

1. 16%

2. The middle 95% of newborn babies weigh between 6.2 and 9 pounds.

3. 2.5%

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

5. 83.85%

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 7.6 pounds, standard deviation of 0.7 pounds

1. What percent of newborn babies weigh more than 8.3 pounds?

7.6 + 0.7 = 8.3.

So more than 1 standard deviation above the mean.

The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

Of those above the mean, 100 - 68 = 32% are more than one standard deviation above the mean. So

16% of newborn babies weigh more than 8.3 pounds.

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

Within 2 standard deviations of the mean, so:

7.6 - 2*0.7 = 6.2 pounds

7.6 + 2*0.7 = 9 pounds.

The middle 95% of newborn babies weigh between 6.2 and 9 pounds.

3. What percent of newborn babies weigh less than 6.2 pounds?

More than 2 standard deviations below the mean, which is 5% of the 50% below the mean, so:

2.5% of newborn babies weigh less than 6.2 pounds.

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

Due to the symmetry of the normal distribution, the mean, so 7.6 pounds.

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

5. What percent of newborn babies weigh between 6.9 and 9.7 pounds?

6.9 = 7.6 - 0.7

9.7 = 7.6 + 3*0.7

Within 1 standard deviation below the mean(68% of the 50% below) and 3 standard deviations above the mean(99.7% of the 50% above). So

83.85% of newborn babies weigh between 6.9 and 9.7 pounds.

d

step-by-step explanation: