Respuesta :
Answer:
The middle 20% of blueberries from this farm have diameters between 5.79 and 5.91 mm
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.
In this problem, we have that:
[tex]\mu = 5.85, \sigma = 0.24[/tex]
Middle 20%
50 - 20/2 = 40th percentile to the 50 + 20/2 = 60th percentile.
We want the 60th percentile, which is the value of X when Z has a pvalue of 0.6. So it is X when Z = 0.253.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.253 = \frac{X - 5.85}{0.24}[/tex]
[tex]X - 5.85 = 0.24*0.253[/tex]
[tex]X = 5.91[/tex]
So the answer is:
The middle 20% of blueberries from this farm have diameters between 5.79 and 5.91 mm
