Question

Suppose for every 100 births in a country, the number of boys follows, approximately, a normal curve with a mean of 54 boys and standard deviation of 5 boys. If the next 100 births in a hospital in this country resulted in 39 boys (and thus 61 girls), would that be unusual

Answer 1

Answer:

Z = -3 means that if the next 100 births in a hospital in this country resulted in 39 boys (and thus 61 girls), it would be considered unusual.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Values of Z of -2 or lower, or 2 or higher are considered unusual.

In this problem, we have that:

$\mu = 54, \sigma = 5$

If the next 100 births in a hospital in this country resulted in 39 boys (and thus 61 girls), would that be unusual

This is Z when X = 39. So

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

$Z = \frac{39 - 54}{5}$

$Z = -3$

Z = -3 means that if the next 100 births in a hospital in this country resulted in 39 boys (and thus 61 girls), it would be considered unusual.