Respuesta :
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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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:
[tex]\mu = 54, \sigma = 5[/tex]
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
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{39 - 54}{5}[/tex]
[tex]Z = -3[/tex]
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.
