Question

A study studied the birth weights of 1,278 babies born in the united states. the mean weight was 3234 grams with a standard deviation of 871 grams. assume that birth weight data are approximately bell-shaped. estimate the number of newborns who weighed between 1492 grams and 4976 grams.

Answer 1

1220 Subtracting the lower boundary of 1492 grams from the mean of 3234 gives you 1742 grams below the mean. Dividing 1742 by the standard deviation of 871 gives you 2 standard deviations below the curve. Now doing the same with the upper limit of 4976 grams also gives you 2 standard deviations above the mean (4976-3234)/871 = 2 So you now look for what percentage of the population lies within 2 standard deviations of the mean. Standard lookup tables will indicate that 95.4499736% of the population will be within 2Ď of the mean. So multiply 1278 by 0.954499736 giving 1219.851. Then round to the nearest whole number and you have an estimated 1220 babies that weigh between 1492 grams and 4976 grams.

Answer 2

The number of newborns who weighed between 1492 grams and 4976 grams are $\boxed{1219}.$

Further Explanation:

Given:

The number of babies born in the United States is 1278.

The mean weight was $3234{\text{ gram}}.$

The standard deviation is $871{\text{ gram}}.$

Explanation:

The empirical rule is used to check that the given data set is normally distributed. The data values should lie within the three standard deviation of the mean.

Empirical rule is defined as follows,

68% data points will lie within the first standard deviation of the mean.

$\boxed{P\left( {\mu - \sigma } \right) = 68\% }$

95.4% data points will lie within the two standard deviation of the mean.

$\boxed{P\left( {\mu - 2\sigma } \right) = 95.4\% }$

99.7% data points will lie within the three standard deviation of the mean.

$\boxed{P\left( {\mu - 3\sigma }\right) = 99.7\% }$

Here, $\mu$ represents the mean and $\sigma$ represents the standard deviation.

Subtract or add two times the standard deviation from the mean then the interval can be expressed as,

$\begin{aligned}{\text{Interval}} &= \mu\pm 2\sigma\\&= 3234 \pm 2 \times 871\\&= 3234 \pm 1742\\&= \left( {1492,4976} \right)\\\end{aligned}$

The number of newborns who weighed between 1492 grams and 4976 grams are $\boxed{1219}.$

Learn more:

1. Learn more about normal distribution brainly.com/question/12698949
2. Learn more about standard normal distribution brainly.com/question/13006989
3. Learn more about confidence interval of meanhttps://brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Confidence Interval

Keywords: study, studied, birth weights, babies,  mean weight, standard deviation, bell-shaped, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion, empirical rule.