Respuesta :
Answer:
The minimum duration for which an apartment remained empty for the company to update the kitchen appliances is 122 days.
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 question, we have that:
[tex]\mu = 85, \sigma = 29[/tex]
What is the minimum duration for which an apartment remained empty for the company to update the kitchen appliances?
Top 10%, which is the 100-10 = 90th percentile.
The 90th percentile is X when Z has a pvalue of 0.9, so X when Z = 1.28. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 85}{29}[/tex]
[tex]X - 85 = 1.28*29[/tex]
[tex]X = 122.12[/tex]
Rounded to the nearest whole number,
The minimum duration for which an apartment remained empty for the company to update the kitchen appliances is 122 days.
