Question

The distribution of head circumference for full term newborn female infants is approximately normal with a mean of 33.8 cm and a standard deviation of 1.2 cm.

Determine the approximate percentage of full term newborn female infants with a head circumference between 31 cm and 36 cm. Enter your answer using two decimal places.

Answer 1

Using the normal distribution, it is found that 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 33.8, \sigma = 1.2$

The proportion of full term newborn female infants with a head circumference between 31 cm and 36 cm is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 31, hence:

X = 36:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{36 - 33.8}{1.2}$

Z = 1.83

Z = 1.83 has a p-value of 0.9664.

X = 31:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{31 - 33.8}{1.2}$

Z = -2.33

Z = -2.33 has a p-value of 0.0099.

0.9664 - 0.0099 = 0.9565.

0.9565 = 95.65% of full term newborn female infants with a head circumference between 31 cm and 36 cm.

More can be learned about the normal distribution at https://brainly.com/question/24537145

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