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350 babies were born at Neo Hospital in the past 6 months. The average weight for the babies was found to be
6.8lbs, with a standard deviation of
0.5lbs.
How many babies would you expect to weigh more than 7.8 lbs?

$350$ babies were born at Neo Hospital in the past $6$ months. The average weight for the babies was found to be $6.8\,\text{lbs}$ , with a standard deviation of $0.5\,\text{lbs}$ . How many babies would you expect to weigh more than $7.8\,\text{lbs}$ ?

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Interpret measures of center and variability

Full solution

Q.

350

babies were born at Neo Hospital in the past

6

months. The average weight for the babies was found to be

6.8\,\text{lbs}

, with a standard deviation of

0.5\,\text{lbs}

. How many babies would you expect to weigh more than

7.8\,\text{lbs}

?

Identify Mean and SD: Identify the mean and standard deviation. $\newline$ The mean weight of the babies is $6.8\,\text{lbs}$ , and the standard deviation is $0.5\,\text{lbs}$ .
Calculate Z-Score: Calculate the z-score for $7.8$ lbs. $\newline$ $Z = \frac{X - \text{mean}}{\text{standard deviation}} = \frac{7.8 - 6.8}{0.5} = 2.0$
Find Percentile: Use the z-score to find the corresponding percentile. $\newline$ A z-score of $2.0$ corresponds to the $97.72$ nd percentile in a standard normal distribution. This means $97.72\%$ of the data falls below $7.8$ lbs.
Calculate Babies: Calculate the number of babies weighing more than $7.8$ lbs. $\newline$ $2.28\%$ of the babies are expected to weigh more than $7.8$ lbs ( $100\% - 97.72\%$ ). $\newline$ Number of babies = $2.28\%$ of $350$ = $0.0228 \times 350 = 7.98$

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