Respuesta :
Answer:
a) 3 kilograms
b) 5.7 kilograms
Step-by-step explanation:
Z-score:
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.
In this question:
[tex]\mu = 3.89, \sigma = 0.68[/tex]
We have to find X for both values of Z.
a) z = -1.35
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.35 = \frac{X - 3.89}{0.68}[/tex]
[tex]X - 3.89 = -1.35*0.68[/tex]
[tex]X = 3[/tex]
3 kilograms
b) z = 2.64
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.64 = \frac{X - 3.89}{0.68}[/tex]
[tex]X - 3.89 = 2.64*0.68[/tex]
[tex]X = 5.7[/tex]
5.7 kilograms
